Examples to find Least Common Multiple by using Prime Factorization Method

Examples to find least common multiple by using prime factorization method are discussed here.

We write the prime factorization of each of the given numbers. Then, the required LCM of these numbers is the product of all different prime factors of the numbers using the greatest power of each common prime factor.

1. What is the least common multiple (L.C.M) of 21 and 49 by using prime factorization method?

Solution:

To find the LCM, multiply all prime factors. But the common factors are included only once.

21 = 3 × 7.

49 = 7 × 7 = 7².

= 3 × 7² = 3 × 7 × 7 = 147.

The required least common multiple (L.C.M) of 21 and 49 = 98.

2. What is the least common multiple (L.C.M) of 36 and 14 by using prime factorization method?

Solution:

To find the LCM, multiply all prime factors. But the common factors are included only once.

36 = 2 × 2 × 3 × 3 = 2² × 3².

14 = 2 × 7.

= 2² × 3² × 7 = 2 × 2 × 3 × 3 × 7 = 252.

The required least common multiple (L.C.M) of 36 and 14 = 252.

3. What is the least common multiple (L.C.M) of 5, 4 and 16 by using prime factorization method?

Solution:

To find the LCM, multiply all prime factors. But the common factors are included only once.

5 = 5 × 1.

4 = 2 × 2.

16 = 2 × 2 × 2 × 2 = 2⁴.

= 2⁴ × 5 = 2 × 2 × 2 × 2 × 5 = 80.

The required least common multiple (L.C.M) of 5, 4 and 16 = 80.

4. Find L.C.M of 504 and 594 by prime factorization method.

Solution:

To find the LCM, multiply all prime factors. But the common factors are included only once.

504 = 2 × 2 × 2 × 3 × 3 × 7 = 2³ × 3³ × 7.

594 = 2 × 3 × 3 × 3 × 11 = 2 × 3³ × 11.

= 2³ × 3³ × 7 × 11 = 2 × 2 × 2 × 3 × 3 × 3 × 7 × 11 = 16632.

The required least common multiple (L.C.M) of 504 and 594 = 16632.

These are the four examples to find least common multiple by using prime factorization method.