What is the Least Common Multiple of 742 and 760?
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 742 and 760 is 281960.
LCM(742,760) = 281960
Least Common Multiple of 742 and 760 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 742 and 760, than apply into the LCM equation.
GCF(742,760) = 2
LCM(742,760) = ( 742 × 760) / 2
LCM(742,760) = 563920 / 2
LCM(742,760) = 281960
Least Common Multiple (LCM) of 742 and 760 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 742 and 760. First we will calculate the prime factors of 742 and 760.
Prime Factorization of 742
Prime factors of 742 are 2, 7, 53. Prime factorization of 742 in exponential form is:
742 = 21 × 71 × 531
Prime Factorization of 760
Prime factors of 760 are 2, 5, 19. Prime factorization of 760 in exponential form is:
760 = 23 × 51 × 191
Now multiplying the highest exponent prime factors to calculate the LCM of 742 and 760.
LCM(742,760) = 23 × 71 × 531 × 51 × 191
LCM(742,760) = 281960
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