What is the Least Common Multiple of 678 and 687?
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 678 and 687 is 155262.
LCM(678,687) = 155262
Least Common Multiple of 678 and 687 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 678 and 687, than apply into the LCM equation.
GCF(678,687) = 3
LCM(678,687) = ( 678 × 687) / 3
LCM(678,687) = 465786 / 3
LCM(678,687) = 155262
Least Common Multiple (LCM) of 678 and 687 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 678 and 687. First we will calculate the prime factors of 678 and 687.
Prime Factorization of 678
Prime factors of 678 are 2, 3, 113. Prime factorization of 678 in exponential form is:
678 = 21 × 31 × 1131
Prime Factorization of 687
Prime factors of 687 are 3, 229. Prime factorization of 687 in exponential form is:
687 = 31 × 2291
Now multiplying the highest exponent prime factors to calculate the LCM of 678 and 687.
LCM(678,687) = 21 × 31 × 1131 × 2291
LCM(678,687) = 155262
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