What is the Least Common Multiple of 321 and 340?
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 321 and 340 is 109140.
LCM(321,340) = 109140
Least Common Multiple of 321 and 340 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 321 and 340, than apply into the LCM equation.
GCF(321,340) = 1
LCM(321,340) = ( 321 × 340) / 1
LCM(321,340) = 109140 / 1
LCM(321,340) = 109140
Least Common Multiple (LCM) of 321 and 340 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 321 and 340. First we will calculate the prime factors of 321 and 340.
Prime Factorization of 321
Prime factors of 321 are 3, 107. Prime factorization of 321 in exponential form is:
321 = 31 × 1071
Prime Factorization of 340
Prime factors of 340 are 2, 5, 17. Prime factorization of 340 in exponential form is:
340 = 22 × 51 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 321 and 340.
LCM(321,340) = 31 × 1071 × 22 × 51 × 171
LCM(321,340) = 109140
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