What is the Least Common Multiple of 1965 and 1970?

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 of 1965 and 1970 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1965 and 1970, than apply into the LCM equation.

GCF(1965,1970) = 5
LCM(1965,1970) = ( 1965 × 1970) / 5
LCM(1965,1970) = 3871050 / 5
LCM(1965,1970) = 774210

Least Common Multiple (LCM) of 1965 and 1970 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1965 and 1970. First we will calculate the prime factors of 1965 and 1970.

Prime Factorization of 1965

Prime Factorization of 1970

Now multiplying the highest exponent prime factors to calculate the LCM of 1965 and 1970.

LCM(1965,1970) = 3¹ × 5¹ × 131¹ × 2¹ × 197¹
LCM(1965,1970) = 774210