What is the Least Common Multiple of 59 and 78?
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 59 and 78 is 4602.
LCM(59,78) = 4602
Least Common Multiple of 59 and 78 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 59 and 78, than apply into the LCM equation.
GCF(59,78) = 1
LCM(59,78) = ( 59 × 78) / 1
LCM(59,78) = 4602 / 1
LCM(59,78) = 4602
Least Common Multiple (LCM) of 59 and 78 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 59 and 78. First we will calculate the prime factors of 59 and 78.
Prime Factorization of 59
Prime factors of 59 are 59. Prime factorization of 59 in exponential form is:
59 = 591
Prime Factorization of 78
Prime factors of 78 are 2, 3, 13. Prime factorization of 78 in exponential form is:
78 = 21 × 31 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 59 and 78.
LCM(59,78) = 591 × 21 × 31 × 131
LCM(59,78) = 4602