What is the Least Common Multiple of 315 and 330?
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 315 and 330 is 6930.
LCM(315,330) = 6930
Least Common Multiple of 315 and 330 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 315 and 330, than apply into the LCM equation.
GCF(315,330) = 15
LCM(315,330) = ( 315 × 330) / 15
LCM(315,330) = 103950 / 15
LCM(315,330) = 6930
Least Common Multiple (LCM) of 315 and 330 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 315 and 330. First we will calculate the prime factors of 315 and 330.
Prime Factorization of 315
Prime factors of 315 are 3, 5, 7. Prime factorization of 315 in exponential form is:
315 = 32 × 51 × 71
Prime Factorization of 330
Prime factors of 330 are 2, 3, 5, 11. Prime factorization of 330 in exponential form is:
330 = 21 × 31 × 51 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 315 and 330.
LCM(315,330) = 32 × 51 × 71 × 21 × 111
LCM(315,330) = 6930
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