# To Find Least Common Multiple by using Prime Factorization Method

This topic would discuss about how to find
the least common multiple by using prime factorization method.

**Steps
to find out the least common multiple by using prime factorization method:**

**Step I:** First find all the prime
factors of the given number

**Step II:** Then write all the prime
factors in exponential form

**Step III:** Then find the product of
highest power of all the prime factors.

Here are few examples to illustrate least common multiple by using prime factorization method:

**1. Find the least common factor of 256 and 224 by using prime factorization method.**

The factors of 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^{8}

The factors of 224 = 2 × 2 × 2 × 2 × 2 × 7 = 2^{5} × 7

The highest power of 2 is 2^{8}

The highest power of 7 is 7

The least common multiple of 256 and 224 = 2^{8} × 5 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 = 1792

**2. Find the least common factor of 105 and 110 by using prime factorization method**

The factors of 105 = 5 × 3 × 7

The factors of 110 = 2 × 5 × 11

The highest power of 2 is 2

The highest power of 3 is 3

The highest power of 5 is 5

The highest power of 7 is 7

The highest power of 11 is 11

The least common multiple of 105 and 110 = 2 × 3 × 5 × 7 ×11 = 2310

**Note:**

Here we can see that there are no common factors hence all the factors of both the number are required to be multiplied to find the L.C.M

**3. Find the least common factor of 48 and 60 by using prime factorization method**

The factors of 48 = 2 × 2 × 2 × 2 × 3 = 2^{4} × 3

The factors of 60 = 2 × 2 × 3 × 5 = 2^{2} × 3 × 5

The highest power of 2 is 2^{4}

The highest power of 3 is 3

The highest power of 5 is 5

The least common multiple of 48 and 60 = 2^{4} × 5 × 3 = 2 × 2 × 2 × 2 × 3 × 5 = 240

**4. Find the least common factor of 21 and 42 by using prime factorization method.**

The factors of 21 = 3 × 7

The factors of 42 = 2 × 3 × 7

The highest power of 2 is 2

The highest power of 3 is 3

The highest power of 7 is 7

The least common multiple of 21 and 42 = 2 × 3 × 7 = 42

**5. Find the least common factor of 44 and 88 by using prime factorization method.**

The factors of 44 are: 2 × 2 × 11 = 2^{2} × 11

The factors of 88 are: 2 × 2 × 2 × 11 = 2^{3} × 11

The highest power of 2 is 2^{3} × 11

The highest power of 11 is 11

The least common multiple of 44 and 88 is 2 × 2 × 2 × 11 = 2^{3} × 11 = 88.

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