What is the Least Common Multiple of 308 and 315?
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 308 and 315 is 13860.
LCM(308,315) = 13860
Least Common Multiple of 308 and 315 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 308 and 315, than apply into the LCM equation.
GCF(308,315) = 7
LCM(308,315) = ( 308 × 315) / 7
LCM(308,315) = 97020 / 7
LCM(308,315) = 13860
Least Common Multiple (LCM) of 308 and 315 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 308 and 315. First we will calculate the prime factors of 308 and 315.
Prime Factorization of 308
Prime factors of 308 are 2, 7, 11. Prime factorization of 308 in exponential form is:
308 = 22 × 71 × 111
Prime Factorization of 315
Prime factors of 315 are 3, 5, 7. Prime factorization of 315 in exponential form is:
315 = 32 × 51 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 308 and 315.
LCM(308,315) = 22 × 71 × 111 × 32 × 51
LCM(308,315) = 13860
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