What is the Least Common Multiple of 298 and 312?
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 298 and 312 is 46488.
LCM(298,312) = 46488
Least Common Multiple of 298 and 312 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 298 and 312, than apply into the LCM equation.
GCF(298,312) = 2
LCM(298,312) = ( 298 × 312) / 2
LCM(298,312) = 92976 / 2
LCM(298,312) = 46488
Least Common Multiple (LCM) of 298 and 312 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 298 and 312. First we will calculate the prime factors of 298 and 312.
Prime Factorization of 298
Prime factors of 298 are 2, 149. Prime factorization of 298 in exponential form is:
298 = 21 × 1491
Prime Factorization of 312
Prime factors of 312 are 2, 3, 13. Prime factorization of 312 in exponential form is:
312 = 23 × 31 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 298 and 312.
LCM(298,312) = 23 × 1491 × 31 × 131
LCM(298,312) = 46488
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