What is the Least Common Multiple of 357 and 364?
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 357 and 364 is 18564.
LCM(357,364) = 18564
Least Common Multiple of 357 and 364 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 357 and 364, than apply into the LCM equation.
GCF(357,364) = 7
LCM(357,364) = ( 357 × 364) / 7
LCM(357,364) = 129948 / 7
LCM(357,364) = 18564
Least Common Multiple (LCM) of 357 and 364 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 357 and 364. First we will calculate the prime factors of 357 and 364.
Prime Factorization of 357
Prime factors of 357 are 3, 7, 17. Prime factorization of 357 in exponential form is:
357 = 31 × 71 × 171
Prime Factorization of 364
Prime factors of 364 are 2, 7, 13. Prime factorization of 364 in exponential form is:
364 = 22 × 71 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 357 and 364.
LCM(357,364) = 31 × 71 × 171 × 22 × 131
LCM(357,364) = 18564
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