Least Common Multiple of 1980 and 1982

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 1982 the smallest integer that is 1962180 that is divisible by both numbers.

Least Common Multiple (LCM) of 1980 and 1982 is 1962180.

LCM(1980,1982) = 1962180

LCM of 1980 and 1982

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

LCM of:
and

Least Common Multiple of 1980 and 1982

LCM of 1980 and 1982 is 1962180

Least common multiple can be found by multiplying the highest exponent prime factors of 1980 and 1982. First we will calculate the prime factors of 1980 and 1982.

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 1982


2 1982
991 991
1

Prime factors of 1982 are 2,991. Prime factorization of 1982 in exponential form is:

1982 = 21×9911

Now multiplying the highest exponent prime factors to calculate the LCM of 1980 and 1982.

LCM(1980,1982) = 22×32×51×111×9911
LCM(1980,1982) = 1962180

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 1982

List of positive integer factors of 1982 that divides 1982 without a remainder.

1, 2, 991, 1982

Least Common Multiple of 1980 and 1982 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 1982, than apply into the LCM equation.

GCF(1980,1982) = 2
LCM(1980,1982) = ( 1980 × 1982) / 2
LCM(1980,1982) = 3924360 / 2
LCM(1980,1982) = 1962180

Properties of LCM 1980 and 1982

(i) The LCM of 1982 and 1980 is associative

LCM of 1980 and 1982 = LCM of 1982 and 1980

Related Least Common Multiples of 1980

Related Least Common Multiples of 1982

Frequently Asked Questions on LCM of 1980 and 1982

1. What is the LCM of 1980 and 1982?

Answer: LCM of 1980 and 1982 is 1962180.

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 1982?

Answer: Factors of 1982 are 1, 2, 991, 1982. There are 4 integers that are factors of 1982. The greatest factor of 1982 is 1982.

4. How to Find the LCM of 1980 and 1982?

Answer:

Least Common Multiple of 1980 and 1982 = 1962180

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 1982

1982 = 2 x 991

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

LCM = 1962180 = 2 x 2 x 3 x 3 x 5 x 11 x 991

Step 4: Therefore, the least common multiple of 1980 and 1982 is 1962180.