What is the Least Common Multiple of 10314 and 10330?
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 10314 and 10330 is 53271810.
LCM(10314,10330) = 53271810
Least Common Multiple of 10314 and 10330 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10314 and 10330, than apply into the LCM equation.
GCF(10314,10330) = 2
LCM(10314,10330) = ( 10314 × 10330) / 2
LCM(10314,10330) = 106543620 / 2
LCM(10314,10330) = 53271810
Least Common Multiple (LCM) of 10314 and 10330 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 10314 and 10330. First we will calculate the prime factors of 10314 and 10330.
Prime Factorization of 10314
Prime factors of 10314 are 2, 3, 191. Prime factorization of 10314 in exponential form is:
10314 = 21 × 33 × 1911
Prime Factorization of 10330
Prime factors of 10330 are 2, 5, 1033. Prime factorization of 10330 in exponential form is:
10330 = 21 × 51 × 10331
Now multiplying the highest exponent prime factors to calculate the LCM of 10314 and 10330.
LCM(10314,10330) = 21 × 33 × 1911 × 51 × 10331
LCM(10314,10330) = 53271810
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