What is the Least Common Multiple of 42129 and 42138?
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 42129 and 42138 is 197247978.
LCM(42129,42138) = 197247978
Least Common Multiple of 42129 and 42138 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42129 and 42138, than apply into the LCM equation.
GCF(42129,42138) = 9
LCM(42129,42138) = ( 42129 × 42138) / 9
LCM(42129,42138) = 1775231802 / 9
LCM(42129,42138) = 197247978
Least Common Multiple (LCM) of 42129 and 42138 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 42129 and 42138. First we will calculate the prime factors of 42129 and 42138.
Prime Factorization of 42129
Prime factors of 42129 are 3, 31, 151. Prime factorization of 42129 in exponential form is:
42129 = 32 × 311 × 1511
Prime Factorization of 42138
Prime factors of 42138 are 2, 3, 2341. Prime factorization of 42138 in exponential form is:
42138 = 21 × 32 × 23411
Now multiplying the highest exponent prime factors to calculate the LCM of 42129 and 42138.
LCM(42129,42138) = 32 × 311 × 1511 × 21 × 23411
LCM(42129,42138) = 197247978
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