Least Common Multiple of 1980 and 1983

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 1983 the smallest integer that is 1308780 that is divisible by both numbers.

Least Common Multiple (LCM) of 1980 and 1983 is 1308780.

LCM(1980,1983) = 1308780

LCM of 1980 and 1983

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

LCM of:
and

Least Common Multiple of 1980 and 1983

LCM of 1980 and 1983 is 1308780

Least common multiple can be found by multiplying the highest exponent prime factors of 1980 and 1983. First we will calculate the prime factors of 1980 and 1983.

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 1983


3 1983
661 661
1

Prime factors of 1983 are 3,661. Prime factorization of 1983 in exponential form is:

1983 = 31×6611

Now multiplying the highest exponent prime factors to calculate the LCM of 1980 and 1983.

LCM(1980,1983) = 22×32×51×111×6611
LCM(1980,1983) = 1308780

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 1983

List of positive integer factors of 1983 that divides 1983 without a remainder.

1, 3, 661, 1983

Least Common Multiple of 1980 and 1983 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 1983, than apply into the LCM equation.

GCF(1980,1983) = 3
LCM(1980,1983) = ( 1980 × 1983) / 3
LCM(1980,1983) = 3926340 / 3
LCM(1980,1983) = 1308780

Properties of LCM 1980 and 1983

(i) The LCM of 1983 and 1980 is associative

LCM of 1980 and 1983 = LCM of 1983 and 1980

Related Least Common Multiples of 1980

Related Least Common Multiples of 1983

Frequently Asked Questions on LCM of 1980 and 1983

1. What is the LCM of 1980 and 1983?

Answer: LCM of 1980 and 1983 is 1308780.

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 1983?

Answer: Factors of 1983 are 1, 3, 661, 1983. There are 4 integers that are factors of 1983. The greatest factor of 1983 is 1983.

4. How to Find the LCM of 1980 and 1983?

Answer:

Least Common Multiple of 1980 and 1983 = 1308780

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 1983

1983 = 3 x 661

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

LCM = 1308780 = 2 x 2 x 3 x 3 x 5 x 11 x 661

Step 4: Therefore, the least common multiple of 1980 and 1983 is 1308780.