What is the Least Common Multiple of 670 and 678?
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 670 and 678 is 227130.
LCM(670,678) = 227130
Least Common Multiple of 670 and 678 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 670 and 678, than apply into the LCM equation.
GCF(670,678) = 2
LCM(670,678) = ( 670 × 678) / 2
LCM(670,678) = 454260 / 2
LCM(670,678) = 227130
Least Common Multiple (LCM) of 670 and 678 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 670 and 678. First we will calculate the prime factors of 670 and 678.
Prime Factorization of 670
Prime factors of 670 are 2, 5, 67. Prime factorization of 670 in exponential form is:
670 = 21 × 51 × 671
Prime Factorization of 678
Prime factors of 678 are 2, 3, 113. Prime factorization of 678 in exponential form is:
678 = 21 × 31 × 1131
Now multiplying the highest exponent prime factors to calculate the LCM of 670 and 678.
LCM(670,678) = 21 × 51 × 671 × 31 × 1131
LCM(670,678) = 227130
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