What is the Least Common Multiple of 312 and 316?
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 312 and 316 is 24648.
LCM(312,316) = 24648
Least Common Multiple of 312 and 316 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 312 and 316, than apply into the LCM equation.
GCF(312,316) = 4
LCM(312,316) = ( 312 × 316) / 4
LCM(312,316) = 98592 / 4
LCM(312,316) = 24648
Least Common Multiple (LCM) of 312 and 316 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 312 and 316. First we will calculate the prime factors of 312 and 316.
Prime Factorization of 312
Prime factors of 312 are 2, 3, 13. Prime factorization of 312 in exponential form is:
312 = 23 × 31 × 131
Prime Factorization of 316
Prime factors of 316 are 2, 79. Prime factorization of 316 in exponential form is:
316 = 22 × 791
Now multiplying the highest exponent prime factors to calculate the LCM of 312 and 316.
LCM(312,316) = 23 × 31 × 131 × 791
LCM(312,316) = 24648
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