The least number which when divided by 16, 24, 36 and 54 leaves in each case a remainder of 6 is

LCM of 24, 36 and 54 is 216. The smallest number among all common multiples of 24, 36, and 54 is the LCM of 24, 36, and 54. (24, 48, 72, 96, 120…), (36, 72, 108, 144, 180…), and (54, 108, 162, 216, 270…), respectively, are the first few multiples of 24, 36, and 54. There are three typical ways for calculating the LCM of 24, 36, and 54: listing multiples, prime factorization, and division. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values.

Nội dung chính

  • What is LCM of 24, 36 and 54?
  • LCM of 24, 36 and 54 Using Prime Factorisation Method
  • LCM of 24, 36 and 54 Using Division Method
  • LCM of 24, 36 and 54 Using Listing the Multiples
  • Related Articles
  • Video Lesson on Applications of LCM
  • LCM of 24, 36 and 54 Solved Example
  • Frequently Asked Questions on LCM of 24, 36 and 54
  • What is the LCM of 24, 36 and 54?
  • List the methods used to find the LCM of 24, 36 and 54.
  • Which of the following is the LCM of 24, 36, and 54? 120, 100, 216, 35
  • What is the Least Perfect Square Divisible by 24, 36, and 54?
  • What is the least number which when divided by 24 and 36?
  • What least number when divided by 36 24 and 16 leaves 11 as remainder in each case ?( Hint find LCM then add 11 to LCM?
  • What is the smallest number which when divided by 24 30 and 54 leaves a remainder of 5 in each case?
  • What is the smallest number which when divided by 27 36 57 gives a remainder of 5 in each case?

Also read: Least common multiple

What is LCM of 24, 36 and 54?

The answer to this question is 216. The LCM of 24, 36 and 54 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24, 36 and 54, is the smallest positive integer 216 which is divisible by both 24, 36 and 54 with no remainder.

LCM of 24, 36 and 54 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 24, 36 and 54 Using Prime Factorisation Method

The prime factorisation of 24, 36 and 54, respectively, is given by:

24 = 2 x 2 x 2 x 3 = 2³x 3

36 = 2 x 2 x 3 x 3 = 2² x 3²

54 = (2 × 3 × 3 × 3) = 21 × 33

LCM (24, 36, 54) = 216

LCM of 24, 36 and 54 Using Division Method

We’ll divide the numbers (24, 36, 54) by their prime factors to get the LCM of 24, 36 and 54 using the division method (preferably common). The LCM of 24, 36 and 54 is calculated by multiplying these divisors.

2 24 36 54
2 12 18 27
2 6 9 27
2 3 9 27
3 1 3 27
3 1 1 9
3 1 1 3
x 1 1 1

No further division can be done.

Hence, LCM (24, 36, 54) = 216

LCM of 24, 36 and 54 Using Listing the Multiples

To calculate the LCM of 24, 36 and 54 by listing out the common multiples, list the multiples as shown below

Multiples of 24 Multiples of 36 Multiples of 54
24 36 54
48 72 108
72 108 162
96 144 216
180 270
216 216 324

The smallest common multiple of 24, 36 and 54 is 216.

Therefore LCM (24, 36, 54) = 216

  • HCF and LCM
  • Prime Factorization
  • LCM calculator
  • Prime Factorization Calculator

Video Lesson on Applications of LCM

LCM of 24, 36 and 54 Solved Example

Find the smallest number that is divisible by 24, 36, 54 exactly.

Solution:

The smallest number that is divisible by 24, 36, and 54 exactly is their LCM.

⇒ Multiples of 24, 36, and 54:

Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, . . . .

Multiples of 36 = 36, 72, 108, 144, 180, 216, . . . .

Multiples of 54 = 54, 108, 162, 216, 270, . . . .

Frequently Asked Questions on LCM of 24, 36 and 54

What is the LCM of 24, 36 and 54?

The LCM of 24, 36, and 54 is 216. To find the least common multiple (LCM) of 24, 36, and 54, we need to find the multiples of 24, 36, and 54 (multiples of 24 = 24, 48, 72, 96 . . . . 216 . . . . ; multiples of 36 = 36, 72, 108, 144, 216 . . . .; multiples of 54 = 54, 108, 162, 216 . . . .) and choose the smallest multiple that is exactly divisible by 24, 36, and 54, i.e., 216.

List the methods used to find the LCM of 24, 36 and 54.

The methods used to find the LCM of 24, 36 and 54 are Prime Factorization Method, Division Method and Listing multiples.

Which of the following is the LCM of 24, 36, and 54? 120, 100, 216, 35

The value of LCM of 24, 36, 54 is the smallest common multiple of 24, 36, and 54. The number satisfying the given condition is 216.

What is the Least Perfect Square Divisible by 24, 36, and 54?

The least number divisible by 24, 36, and 54 = LCM(24, 36, 54)
LCM of 24, 36, and 54 = 2 × 2 × 2 × 3 × 3 × 3 [Incomplete pair(s): 2, 3] ⇒ Least perfect square divisible by each 24, 36, and 54 = LCM(24, 36, 54) × 2 × 3 = 1296 [Square root of 1296 = √1296 = ±36] Therefore, 1296 is the required number.

Therefore, the LCM of 24, 36, and 54 is 216.

What is the least number which when divided by 24 and 36?

Hence a- 3 is the smallest number with the above properties.

What least number when divided by 36 24 and 16 leaves 11 as remainder in each case ?( Hint find LCM then add 11 to LCM?

This is Expert Verified Answer 155 is the least number when divided by 36, 24 and 16 leaves 11 as remainder in each case. 144 is the LCM of 36, 24 and 16. ∴ 155 is the least number when divided by 36, 24 and 16 leaves 11 as remainder in each case.

What is the smallest number which when divided by 24 30 and 54 leaves a remainder of 5 in each case?

Step-by-step explanation: LCM(24, 30, 54)= 2*2*2*3*3*3*5=1080.

What is the smallest number which when divided by 27 36 57 gives a remainder of 5 in each case?

Answer. Answer: The smaller number which 27,36 and 57 is 18. The reminder of 5 in each case is 113.

What is the least number which when divided by 24 36 and 54 gives a remainder of 5 each time?

What is the smallest number which when divided by 24, 36 and 54 gives a remainder of 5 each time? Therefore, the smallest number which when divided by 24, 26 and 54 gives a remainder of 5 each time is 221.

What is the least number which when divided by 12 16 24 36 leaves a remainder 7 in each case?

Least Number which when divided by 12, 16 ,24 and 36 leaves a remainder 7 in each case =144+7=151.

What is the least number when divided by 36 24 16 leaves 11 as remainder in each case?

This is Expert Verified Answer 155 is the least number when divided by 36, 24 and 16 leaves 11 as remainder in each case. 144 is the LCM of 36, 24 and 16. ∴ 155 is the least number when divided by 36, 24 and 16 leaves 11 as remainder in each case.

Which is the smallest number which when divided by 16 24 or 32 the remainder is 4 in each case?

Least no. that is divisible by 16,24,32,48= L.C.M of 16,24,32,48. L.C.M of 16,24,32,48 = 480. SO the least number divisible by 16,24,32,48 = 480.