Least Common Multiple of 1965 and 1970

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1965 and 1970 the smallest integer that is 774210 that is divisible by both numbers.

Least Common Multiple (LCM) of 1965 and 1970 is 774210.

LCM(1965,1970) = 774210

LCM of 1965 and 1970

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 1965 and 1970

LCM of 1965 and 1970 is 774210

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


3 1965
5 655
131 131
1

Prime factors of 1965 are 3, 5,131. Prime factorization of 1965 in exponential form is:

1965 = 31×51×1311

Prime Factorization of 1970


2 1970
5 985
197 197
1

Prime factors of 1970 are 2, 5,197. Prime factorization of 1970 in exponential form is:

1970 = 21×51×1971

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

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

Factors of 1965

List of positive integer factors of 1965 that divides 1965 without a remainder.

1, 3, 5, 15, 131, 393, 655, 1965

Factors of 1970

List of positive integer factors of 1970 that divides 1970 without a remainder.

1, 2, 5, 10, 197, 394, 985, 1970

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

Properties of LCM 1965 and 1970

(i) The LCM of 1970 and 1965 is associative

LCM of 1965 and 1970 = LCM of 1970 and 1965

Related Least Common Multiples of 1965

Related Least Common Multiples of 1970

Frequently Asked Questions on LCM of 1965 and 1970

1. What is the LCM of 1965 and 1970?

Answer: LCM of 1965 and 1970 is 774210.

2. What are the Factors of 1965?

Answer: Factors of 1965 are 1, 3, 5, 15, 131, 393, 655, 1965. There are 8 integers that are factors of 1965. The greatest factor of 1965 is 1965.

3. What are the Factors of 1970?

Answer: Factors of 1970 are 1, 2, 5, 10, 197, 394, 985, 1970. There are 8 integers that are factors of 1970. The greatest factor of 1970 is 1970.

4. How to Find the LCM of 1965 and 1970?

Answer:

Least Common Multiple of 1965 and 1970 = 774210

Step 1: Find the prime factorization of 1965

1965 = 3 x 5 x 131

Step 2: Find the prime factorization of 1970

1970 = 2 x 5 x 197

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 774210 = 2 x 3 x 5 x 131 x 197

Step 4: Therefore, the least common multiple of 1965 and 1970 is 774210.