# Examples to find Least Common Multiple by using Prime Factorization Method

This topic would provide various examples on
finding the least common multiple using the method of prime factorization.

**Here are few examples
illustrated on finding the least common multiple using the prime factorization
method.**

**1.** Find the least common multiple (L.C.M) of 105 and 124 by prime factorization method

The factors of 105 = 5 × 3 × 7

The factors of 124 = 2 × 2 × 31 = 2^{2} × 31

The prime factors are 2, 3, 5, 7 and 31

The highest power of 2 is 2^{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 31 is 31

The least common multiple of 105 and 124 is 2^{2} × 5 × 3 × 7 × 31 = 13020

**2.** Find the least common multiple (L.C.M) of 18 and 30 by prime factorization method

The factors of 18 are: 2 × 3 × 3 = 2 × 3^{2}

The factors of 30 are: 2 × 3 × 5

The prime factors are 2, 3, and 5

The highest power of 2 is 2

The highest power of 3 is 3^{2}

The highest power of 5 is 5

The least common multiple of 18 and 30 is 2 × 3^{2} × 5 = 2 × 3 × 3 × 5 = 90

**3.** Find the least common multiple (L.C.M) of 180 and 220 by prime factorization method

The factors of 180 are: 2 × 2 × 3 × 3 × 5 = 2^{2} × 3^{2} × 5

The factors of 220 are: 2 × 2 × 5 × 11 = 2^{2} × 5 × 11

The prime factors are 2, 3, and 5

The highest power of 2 is 2^{2}

The highest power of 3 is 3^{2}

The highest power of 5 is 5

The highest power of 11 is 11

The least common multiple of 180 and 220 is 2^{2} × 3^{2} ×5 × 11= 2 × 2 × 3 × 3 × 5 × 11 = 1980

**4.** Find the least common multiple (L.C.M) of 360 and 520 by prime factorization method:

The factors of 360 are: 2 × 2 × 2 × 3 × 3 × 5 = 2^{3} × 3^{2} × 5

The factors of 520 are: 2 × 2 × 2 × 5 × 13 = 2^{3} × 5 × 13

The prime factors are 2, 3, 5 and 13

The highest power of 2 is 2^{3}

The highest power of 3 is 3^{2}

The highest power of 5 is 5

The highest power of 13 is 13

The least common multiple of 360 and 520 is 2^{3} × 3^{2} × 5 × 13 = 2 × 2 × 2 × 3 × 3 × 5 × 13 = 4680

**5.** Find the least common multiple (L.C.M) of 44 and 88 by 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 prime factors are 2 and 11

The highest power of 2 is 2^{3}

The highest power of 11 is 11

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

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