What is the Least Common Multiple of 685 and 705?
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 685 and 705 is 96585.
LCM(685,705) = 96585
Least Common Multiple of 685 and 705 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 685 and 705, than apply into the LCM equation.
GCF(685,705) = 5
LCM(685,705) = ( 685 × 705) / 5
LCM(685,705) = 482925 / 5
LCM(685,705) = 96585
Least Common Multiple (LCM) of 685 and 705 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 685 and 705. First we will calculate the prime factors of 685 and 705.
Prime Factorization of 685
Prime factors of 685 are 5, 137. Prime factorization of 685 in exponential form is:
685 = 51 × 1371
Prime Factorization of 705
Prime factors of 705 are 3, 5, 47. Prime factorization of 705 in exponential form is:
705 = 31 × 51 × 471
Now multiplying the highest exponent prime factors to calculate the LCM of 685 and 705.
LCM(685,705) = 51 × 1371 × 31 × 471
LCM(685,705) = 96585
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