What is the Least Common Multiple of 684 and 693?
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 684 and 693 is 52668.
LCM(684,693) = 52668
Least Common Multiple of 684 and 693 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 684 and 693, than apply into the LCM equation.
GCF(684,693) = 9
LCM(684,693) = ( 684 × 693) / 9
LCM(684,693) = 474012 / 9
LCM(684,693) = 52668
Least Common Multiple (LCM) of 684 and 693 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 684 and 693. First we will calculate the prime factors of 684 and 693.
Prime Factorization of 684
Prime factors of 684 are 2, 3, 19. Prime factorization of 684 in exponential form is:
684 = 22 × 32 × 191
Prime Factorization of 693
Prime factors of 693 are 3, 7, 11. Prime factorization of 693 in exponential form is:
693 = 32 × 71 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 684 and 693.
LCM(684,693) = 22 × 32 × 191 × 71 × 111
LCM(684,693) = 52668
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