What is the Least Common Multiple of 65670 and 65678?
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 65670 and 65678 is 2156537130.
LCM(65670,65678) = 2156537130
Least Common Multiple of 65670 and 65678 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65670 and 65678, than apply into the LCM equation.
GCF(65670,65678) = 2
LCM(65670,65678) = ( 65670 × 65678) / 2
LCM(65670,65678) = 4313074260 / 2
LCM(65670,65678) = 2156537130
Least Common Multiple (LCM) of 65670 and 65678 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 65670 and 65678. First we will calculate the prime factors of 65670 and 65678.
Prime Factorization of 65670
Prime factors of 65670 are 2, 3, 5, 11, 199. Prime factorization of 65670 in exponential form is:
65670 = 21 × 31 × 51 × 111 × 1991
Prime Factorization of 65678
Prime factors of 65678 are 2, 32839. Prime factorization of 65678 in exponential form is:
65678 = 21 × 328391
Now multiplying the highest exponent prime factors to calculate the LCM of 65670 and 65678.
LCM(65670,65678) = 21 × 31 × 51 × 111 × 1991 × 328391
LCM(65670,65678) = 2156537130
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