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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