# To find Least Common Multiple by using Prime Factorization Method

To find least common multiple by using prime factorization method is discussed here.

Step I:

Resolve each given number into its prime factors and express the factors obtained in exponent form.

Step I:

Find the product of the highest powers of all the factors that occur in any of the given numbers.

Step III:

The product obtained in Step II is the required least common multiple (L.C.M).

For example:

1. Find the least common multiple (L.C.M) of 9 and 15 by using prime factorization method.

Solution:

Step I:

Resolving each given number into its prime factors. 9 = 3 × 3 = 3².

15 = 3 × 5.

Step II:

The product of all the factors with highest powers.

= 3^2 × 5 = 3 × 3 × 5 = 45.

Step III:

The required least common multiple (L.C.M) of 9 and 15 = 45.

2. What is the least common multiple (L.C.M) of 16 and 28 by using prime factorization method?

Solution:

Step I:

Resolving each given number into its prime factors. 16 = 2 × 2 × 2 × 2 = 2⁴.

28 = 2 × 2 × 7 = 2² × 7.

Step II:

The product of all the factors with highest powers.

= 2^4 × 7 = 2 × 2 × 2 × 2 ×7 = 112.

Step III:

The required least common multiple (L.C.M) of 16 and 28 = 112.

To Find Lowest Common Multiple by using Division Method

Relationship between H.C.F. and L.C.M.

Worksheet on H.C.F. and L.C.M.

Word problems on H.C.F. and L.C.M.

Worksheet on word problems on H.C.F. and L.C.M.