What is the Least Common Multiple of 123 and 138?
Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.
Least common multiple (LCM) of 123 and 138 is 5658.
LCM(123,138) = 5658
Least Common Multiple of 123 and 138 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 123 and 138, than apply into the LCM equation.
GCF(123,138) = 3
LCM(123,138) = ( 123 × 138) / 3
LCM(123,138) = 16974 / 3
LCM(123,138) = 5658
Least Common Multiple (LCM) of 123 and 138 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 123 and 138. First we will calculate the prime factors of 123 and 138.
Prime Factorization of 123
Prime factors of 123 are 3, 41. Prime factorization of 123 in exponential form is:
123 = 31 × 411
Prime Factorization of 138
Prime factors of 138 are 2, 3, 23. Prime factorization of 138 in exponential form is:
138 = 21 × 31 × 231
Now multiplying the highest exponent prime factors to calculate the LCM of 123 and 138.
LCM(123,138) = 31 × 411 × 21 × 231
LCM(123,138) = 5658
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