Least Common Multiple of 1965 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 1965 and 1972 the smallest integer that is 3874980 that is divisible by both numbers.

Least Common Multiple (LCM) of 1965 and 1972 is 3874980.

LCM(1965,1972) = 3874980

LCM of 1965 and 1972

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

LCM of:
and

Least Common Multiple of 1965 and 1972

LCM of 1965 and 1972 is 3874980

Least common multiple can be found by multiplying the highest exponent prime factors of 1965 and 1972. First we will calculate the prime factors of 1965 and 1972.

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 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 1965 and 1972.

LCM(1965,1972) = 22×31×51×171×291×1311
LCM(1965,1972) = 3874980

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 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 1965 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 1965 and 1972, than apply into the LCM equation.

GCF(1965,1972) = 1
LCM(1965,1972) = ( 1965 × 1972) / 1
LCM(1965,1972) = 3874980 / 1
LCM(1965,1972) = 3874980

Properties of LCM 1965 and 1972

(i) The LCM of 1972 and 1965 is associative

LCM of 1965 and 1972 = LCM of 1972 and 1965

Related Least Common Multiples of 1965

Related Least Common Multiples of 1972

Frequently Asked Questions on LCM of 1965 and 1972

1. What is the LCM of 1965 and 1972?

Answer: LCM of 1965 and 1972 is 3874980.

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 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 1965 and 1972?

Answer:

Least Common Multiple of 1965 and 1972 = 3874980

Step 1: Find the prime factorization of 1965

1965 = 3 x 5 x 131

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 = 3874980 = 2 x 2 x 3 x 5 x 17 x 29 x 131

Step 4: Therefore, the least common multiple of 1965 and 1972 is 3874980.