Least Common Multiple of 1976 and 1980

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1976 and 1980 the smallest integer that is 978120 that is divisible by both numbers.

Least Common Multiple (LCM) of 1976 and 1980 is 978120.

LCM(1976,1980) = 978120

LCM of 1976 and 1980

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

LCM of:
and

Least Common Multiple of 1976 and 1980

LCM of 1976 and 1980 is 978120

Least common multiple can be found by multiplying the highest exponent prime factors of 1976 and 1980. First we will calculate the prime factors of 1976 and 1980.

Prime Factorization of 1976


2 1976
2 988
2 494
13 247
19 19
1

Prime factors of 1976 are 2, 13,19. Prime factorization of 1976 in exponential form is:

1976 = 23×131×191

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1976 and 1980.

LCM(1976,1980) = 23×32×51×111×131×191
LCM(1976,1980) = 978120

Factors of 1976

List of positive integer factors of 1976 that divides 1976 without a remainder.

1, 2, 4, 8, 13, 19, 26, 38, 52, 76, 104, 152, 247, 494, 988, 1976

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

Least Common Multiple of 1976 and 1980 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1976 and 1980, than apply into the LCM equation.

GCF(1976,1980) = 4
LCM(1976,1980) = ( 1976 × 1980) / 4
LCM(1976,1980) = 3912480 / 4
LCM(1976,1980) = 978120

Properties of LCM 1976 and 1980

(i) The LCM of 1980 and 1976 is associative

LCM of 1976 and 1980 = LCM of 1980 and 1976

Related Least Common Multiples of 1976

Related Least Common Multiples of 1980

Frequently Asked Questions on LCM of 1976 and 1980

1. What is the LCM of 1976 and 1980?

Answer: LCM of 1976 and 1980 is 978120.

2. What are the Factors of 1976?

Answer: Factors of 1976 are 1, 2, 4, 8, 13, 19, 26, 38, 52, 76, 104, 152, 247, 494, 988, 1976. There are 16 integers that are factors of 1976. The greatest factor of 1976 is 1976.

3. 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.

4. How to Find the LCM of 1976 and 1980?

Answer:

Least Common Multiple of 1976 and 1980 = 978120

Step 1: Find the prime factorization of 1976

1976 = 2 x 2 x 2 x 13 x 19

Step 2: Find the prime factorization of 1980

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

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

LCM = 978120 = 2 x 2 x 2 x 3 x 3 x 5 x 11 x 13 x 19

Step 4: Therefore, the least common multiple of 1976 and 1980 is 978120.