Least Common Multiple of 1964 and 1972

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1964 and 1972 the smallest integer that is 968252 that is divisible by both numbers.

Least Common Multiple (LCM) of 1964 and 1972 is 968252.

LCM(1964,1972) = 968252

LCM of 1964 and 1972

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

LCM of:
and

Least Common Multiple of 1964 and 1972

LCM of 1964 and 1972 is 968252

Least common multiple can be found by multiplying the highest exponent prime factors of 1964 and 1972. First we will calculate the prime factors of 1964 and 1972.

Prime Factorization of 1964


2 1964
2 982
491 491
1

Prime factors of 1964 are 2,491. Prime factorization of 1964 in exponential form is:

1964 = 22×4911

Prime Factorization of 1972


2 1972
2 986
17 493
29 29
1

Prime factors of 1972 are 2, 17,29. Prime factorization of 1972 in exponential form is:

1972 = 22×171×291

Now multiplying the highest exponent prime factors to calculate the LCM of 1964 and 1972.

LCM(1964,1972) = 22×171×291×4911
LCM(1964,1972) = 968252

Factors of 1964

List of positive integer factors of 1964 that divides 1964 without a remainder.

1, 2, 4, 491, 982, 1964

Factors of 1972

List of positive integer factors of 1972 that divides 1972 without a remainder.

1, 2, 4, 17, 29, 34, 58, 68, 116, 493, 986, 1972

Least Common Multiple of 1964 and 1972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1964 and 1972, than apply into the LCM equation.

GCF(1964,1972) = 4
LCM(1964,1972) = ( 1964 × 1972) / 4
LCM(1964,1972) = 3873008 / 4
LCM(1964,1972) = 968252

Properties of LCM 1964 and 1972

(i) The LCM of 1972 and 1964 is associative

LCM of 1964 and 1972 = LCM of 1972 and 1964

Related Least Common Multiples of 1964

Related Least Common Multiples of 1972

Frequently Asked Questions on LCM of 1964 and 1972

1. What is the LCM of 1964 and 1972?

Answer: LCM of 1964 and 1972 is 968252.

2. What are the Factors of 1964?

Answer: Factors of 1964 are 1, 2, 4, 491, 982, 1964. There are 6 integers that are factors of 1964. The greatest factor of 1964 is 1964.

3. What are the Factors of 1972?

Answer: Factors of 1972 are 1, 2, 4, 17, 29, 34, 58, 68, 116, 493, 986, 1972. There are 12 integers that are factors of 1972. The greatest factor of 1972 is 1972.

4. How to Find the LCM of 1964 and 1972?

Answer:

Least Common Multiple of 1964 and 1972 = 968252

Step 1: Find the prime factorization of 1964

1964 = 2 x 2 x 491

Step 2: Find the prime factorization of 1972

1972 = 2 x 2 x 17 x 29

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

LCM = 968252 = 2 x 2 x 17 x 29 x 491

Step 4: Therefore, the least common multiple of 1964 and 1972 is 968252.