Least Common Multiple of 1965 and 1971

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 1971 the smallest integer that is 1291005 that is divisible by both numbers.

Least Common Multiple (LCM) of 1965 and 1971 is 1291005.

LCM(1965,1971) = 1291005

LCM of 1965 and 1971

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

LCM of:
and

Least Common Multiple of 1965 and 1971

LCM of 1965 and 1971 is 1291005

Least common multiple can be found by multiplying the highest exponent prime factors of 1965 and 1971. First we will calculate the prime factors of 1965 and 1971.

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 1971


3 1971
3 657
3 219
73 73
1

Prime factors of 1971 are 3,73. Prime factorization of 1971 in exponential form is:

1971 = 33×731

Now multiplying the highest exponent prime factors to calculate the LCM of 1965 and 1971.

LCM(1965,1971) = 33×51×731×1311
LCM(1965,1971) = 1291005

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 1971

List of positive integer factors of 1971 that divides 1971 without a remainder.

1, 3, 9, 27, 73, 219, 657, 1971

Least Common Multiple of 1965 and 1971 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 1971, than apply into the LCM equation.

GCF(1965,1971) = 3
LCM(1965,1971) = ( 1965 × 1971) / 3
LCM(1965,1971) = 3873015 / 3
LCM(1965,1971) = 1291005

Properties of LCM 1965 and 1971

(i) The LCM of 1971 and 1965 is associative

LCM of 1965 and 1971 = LCM of 1971 and 1965

Related Least Common Multiples of 1965

Related Least Common Multiples of 1971

Frequently Asked Questions on LCM of 1965 and 1971

1. What is the LCM of 1965 and 1971?

Answer: LCM of 1965 and 1971 is 1291005.

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 1971?

Answer: Factors of 1971 are 1, 3, 9, 27, 73, 219, 657, 1971. There are 8 integers that are factors of 1971. The greatest factor of 1971 is 1971.

4. How to Find the LCM of 1965 and 1971?

Answer:

Least Common Multiple of 1965 and 1971 = 1291005

Step 1: Find the prime factorization of 1965

1965 = 3 x 5 x 131

Step 2: Find the prime factorization of 1971

1971 = 3 x 3 x 3 x 73

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

LCM = 1291005 = 3 x 3 x 3 x 5 x 73 x 131

Step 4: Therefore, the least common multiple of 1965 and 1971 is 1291005.