LCM of 8, 16 and 24

LCM of 8, 16 and 24 is 48. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Least common multiple of 8, 16 and 24 is the smallest number we get among the common multiples. The first few multiples of 8, 16, and 24 are (8, 16, 24, 32, 40 . . .), (16, 32, 48, 64, 80 . . .), and (24, 48, 72, 96, 120 . . .) respectively. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.

Also read: Least common multiple

What is LCM of 8, 16 and 24?

The answer to this question is 48. The LCM of 8, 16 and 24 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8, 16 and 24, is the smallest positive integer 48 which is divisible by both 8, 16 and 24 with no remainder.

lcm of 8 16 and 24

How to Find LCM of 8, 16 and 24?

LCM of 8, 16 and 24 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 8, 16 and 24 Using Prime Factorisation Method

The prime factorisation of 8, 16 and 24, respectively, is given by:

8 = (2 × 2 × 2) = 23,

16 = (2 × 2 × 2 × 2) = 24, and

24 = (2 × 2 × 2 × 3) = 23 × 31

LCM (8, 16, 24) = 48

LCM of 8, 16 and 24 Using Division Method

We’ll divide the numbers (8, 16, 24) by their prime factors to get the LCM of 8, 16 and 24 using the division method (preferably common). The LCM of 8, 16 and 24 is calculated by multiplying these divisors.

2 8 16 24
2 4 8 12
2 2 4 6
2 1 2 3
3 1 1 3
x 1 1 1

No further division can be done.

Hence, LCM (8, 16, 24) = 48

LCM of 8, 16 and 24 Using Listing the Multiples

To calculate the LCM of 8, 16 and 24 by listing out the common multiples, list the multiples as shown below.

Multiples of 8 Multiples of 16 Multiples of 24
8 16 24
16 32 48
24 48 72
32 64 96
40 80 120
48 96 144

The smallest common multiple of 8, 16 and 24 is 48.

Therefore LCM (8, 16, 24) = 48

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LCM of 8, 16 and 24 Solved Example

Question: Find the smallest number that is divisible by 8, 16, 24 exactly.

Solution:

The smallest number that is divisible by 8, 16, and 24 exactly is their LCM.

⇒ Multiples of 8, 16, and 24:

Multiples of 8 = 8, 16, 24, 32, 40, 48, . . . .

Multiples of 16 = 16, 32, 48, 64, 80, 96, . . . .

Multiples of 24 = 24, 48, 72, 96, 120, 144, . . . .

Therefore, the LCM of 8, 16, and 24 is 48.

Frequently Asked Questions on LCM of 8, 16 and 24

Q1

What is the LCM of 8, 16 and 24?

The LCM of 8, 16, and 24 is 48. To find the LCM of 8, 16, and 24, we need to find the multiples of 8, 16, and 24 (multiples of 8 = 8, 16, 24, 32, 48 . . . .; multiples of 16 = 16, 32, 48, 64 . . . .; multiples of 24 = 24, 48, 72, 96 . . . .) and choose the smallest multiple that is exactly divisible by 8, 16, and 24, i.e., 48.
Q2

List the methods used to find the LCM of 8, 16 and 24.

The methods used to find the LCM of 8, 16 and 24 are Prime Factorization Method, Division Method and Listing multiples.
Q3

What is the Relation Between GCF and LCM of 8, 16, 24?

The following equation can be used to express the relation between GCF and LCM of 8, 16, 24, i.e. LCM(8, 16, 24) = [(8 × 16 × 24) × GCF(8, 16, 24)]/[GCF(8, 16) × GCF(16, 24) × GCF(8, 24)].

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