Least Common Multiple of 1980 and 1987

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1980 and 1987 the smallest integer that is 3934260 that is divisible by both numbers.

Least Common Multiple (LCM) of 1980 and 1987 is 3934260.

LCM(1980,1987) = 3934260

LCM of 1980 and 1987

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

LCM of:
and

Least Common Multiple of 1980 and 1987

LCM of 1980 and 1987 is 3934260

Least common multiple can be found by multiplying the highest exponent prime factors of 1980 and 1987. First we will calculate the prime factors of 1980 and 1987.

Prime Factorization of 1980


2 1980
2 990
3 495
3 165
5 55
11 11
1

Prime factors of 1980 are 2, 3, 5,11. Prime factorization of 1980 in exponential form is:

1980 = 22×32×51×111

Prime Factorization of 1987


1987 1987
1

Prime factors of 1987 are 1987. Prime factorization of 1987 in exponential form is:

1987 = 19871

Now multiplying the highest exponent prime factors to calculate the LCM of 1980 and 1987.

LCM(1980,1987) = 22×32×51×111×19871
LCM(1980,1987) = 3934260

Factors of 1980

List of positive integer factors of 1980 that divides 1980 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980

Factors of 1987

List of positive integer factors of 1987 that divides 1987 without a remainder.

1, 1987

Least Common Multiple of 1980 and 1987 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1980 and 1987, than apply into the LCM equation.

GCF(1980,1987) = 1
LCM(1980,1987) = ( 1980 × 1987) / 1
LCM(1980,1987) = 3934260 / 1
LCM(1980,1987) = 3934260

Properties of LCM 1980 and 1987

(i) The LCM of 1987 and 1980 is associative

LCM of 1980 and 1987 = LCM of 1987 and 1980

Related Least Common Multiples of 1980

Related Least Common Multiples of 1987

Frequently Asked Questions on LCM of 1980 and 1987

1. What is the LCM of 1980 and 1987?

Answer: LCM of 1980 and 1987 is 3934260.

2. What are the Factors of 1980?

Answer: Factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980. There are 36 integers that are factors of 1980. The greatest factor of 1980 is 1980.

3. What are the Factors of 1987?

Answer: Factors of 1987 are 1, 1987. There are 2 integers that are factors of 1987. The greatest factor of 1987 is 1987.

4. How to Find the LCM of 1980 and 1987?

Answer:

Least Common Multiple of 1980 and 1987 = 3934260

Step 1: Find the prime factorization of 1980

1980 = 2 x 2 x 3 x 3 x 5 x 11

Step 2: Find the prime factorization of 1987

1987 = 1987

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

LCM = 3934260 = 2 x 2 x 3 x 3 x 5 x 11 x 1987

Step 4: Therefore, the least common multiple of 1980 and 1987 is 3934260.