What is the Least Common Multiple of 123 and 134?
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 134 is 16482.
LCM(123,134) = 16482
Least Common Multiple of 123 and 134 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 134, than apply into the LCM equation.
GCF(123,134) = 1
LCM(123,134) = ( 123 × 134) / 1
LCM(123,134) = 16482 / 1
LCM(123,134) = 16482
Least Common Multiple (LCM) of 123 and 134 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 123 and 134. First we will calculate the prime factors of 123 and 134.
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 134
Prime factors of 134 are 2, 67. Prime factorization of 134 in exponential form is:
134 = 21 × 671
Now multiplying the highest exponent prime factors to calculate the LCM of 123 and 134.
LCM(123,134) = 31 × 411 × 21 × 671
LCM(123,134) = 16482
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