What is the Least Common Multiple of 682 and 688?
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 682 and 688 is 234608.
LCM(682,688) = 234608
Least Common Multiple of 682 and 688 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 682 and 688, than apply into the LCM equation.
GCF(682,688) = 2
LCM(682,688) = ( 682 × 688) / 2
LCM(682,688) = 469216 / 2
LCM(682,688) = 234608
Least Common Multiple (LCM) of 682 and 688 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 682 and 688. First we will calculate the prime factors of 682 and 688.
Prime Factorization of 682
Prime factors of 682 are 2, 11, 31. Prime factorization of 682 in exponential form is:
682 = 21 × 111 × 311
Prime Factorization of 688
Prime factors of 688 are 2, 43. Prime factorization of 688 in exponential form is:
688 = 24 × 431
Now multiplying the highest exponent prime factors to calculate the LCM of 682 and 688.
LCM(682,688) = 24 × 111 × 311 × 431
LCM(682,688) = 234608
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