What is the Least Common Multiple of 339 and 354?
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 339 and 354 is 40002.
LCM(339,354) = 40002
Least Common Multiple of 339 and 354 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 339 and 354, than apply into the LCM equation.
GCF(339,354) = 3
LCM(339,354) = ( 339 × 354) / 3
LCM(339,354) = 120006 / 3
LCM(339,354) = 40002
Least Common Multiple (LCM) of 339 and 354 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 339 and 354. First we will calculate the prime factors of 339 and 354.
Prime Factorization of 339
Prime factors of 339 are 3, 113. Prime factorization of 339 in exponential form is:
339 = 31 × 1131
Prime Factorization of 354
Prime factors of 354 are 2, 3, 59. Prime factorization of 354 in exponential form is:
354 = 21 × 31 × 591
Now multiplying the highest exponent prime factors to calculate the LCM of 339 and 354.
LCM(339,354) = 31 × 1131 × 21 × 591
LCM(339,354) = 40002
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