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LCM of 24 and 36: How to find LCM of 24 and 36?

The LCM of 24 and 36 is 72. Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both. The LCM of 24 and 36 is the smallest number that both 24 and 36 go into evenly. In this blog, we will explore easy ways to find the LCM of 24 and 36.

Methods to find the LCM of 24 and 36

Here are three simple methods to calculate the LCM of 24 and 36:

1. Prime Factorization Method

In this method, we break each number into its prime factors and use the highest powers of each factor.

  • Prime factorization of 24: 2 × 2 × 2 × 3
  • Prime factorization of 36: 2 × 2 × 3 × 3
  • Taking the highest powers of all factors: 2³ × 3² = 72

Thus, LCM(24,36) = 72.

2. Listing Multiples Method

We list the multiples of both numbers and find the smallest one that appears in both lists.

  • Multiples of 24: 24, 48, 72, 96, 120, ...
  • Multiples of 36: 36, 72, 108, 144, ...
  • The smallest common multiple is 72.

Thus, LCM(24,36) = 72.

3. Division Method

In this method, we divide both numbers by their common factors until at least 2 numbers are divisible.

  1. Divide 24 and 36 by 2 → (12, 18)
  2. Divide 12 and 18 by 2 → (6, 9)
  3. Divide 6 and 9 by 3 → (2, 3)
  4. 2 and 3 are only divisible by 1.
  5. Multiply the divisors: 2 × 2 × 2 × 3 × 3 = 72

Thus, LCM(24,36) = 72.

Know how to find the lcm of 96 and 404 here.

Conclusion:

The LCM of 24 and 36 is 72, and you can find it using prime factorization, listing multiples, or division. These simple methods make LCM calculations easy and useful for solving math problems.

FAQs

1. What is the LCM of 24 and 36?

The LCM of 24 and 36 is 72.
It is the smallest number that both 24 and 36 divide into without leaving a remainder.

2. What is the LCM of 24 and 36 step by step?

Use the listing method:

  • Multiples of 24: 24, 48, 72, 96...

  • Multiples of 36: 36, 72, 108...
    LCM = 72, the first common multiple.

3. How to find LCM by division method?

  1. Write 24 and 36 side by side.

  2. Divide both by common prime numbers (like 2 or 3) until only 1s or prime numbers remain.

  3. Multiply all the divisors used.
    Example: LCM(24, 36)=2×2×2×3×3=72

 

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