Least Common Multiple of 1977 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 1977 and 1980 the smallest integer that is 1304820 that is divisible by both numbers.

Least Common Multiple (LCM) of 1977 and 1980 is 1304820.

LCM(1977,1980) = 1304820

LCM of 1977 and 1980

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

LCM of:
and

Least Common Multiple of 1977 and 1980

LCM of 1977 and 1980 is 1304820

Least common multiple can be found by multiplying the highest exponent prime factors of 1977 and 1980. First we will calculate the prime factors of 1977 and 1980.

Prime Factorization of 1977


3 1977
659 659
1

Prime factors of 1977 are 3,659. Prime factorization of 1977 in exponential form is:

1977 = 31×6591

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 1977 and 1980.

LCM(1977,1980) = 22×32×51×111×6591
LCM(1977,1980) = 1304820

Factors of 1977

List of positive integer factors of 1977 that divides 1977 without a remainder.

1, 3, 659, 1977

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 1977 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 1977 and 1980, than apply into the LCM equation.

GCF(1977,1980) = 3
LCM(1977,1980) = ( 1977 × 1980) / 3
LCM(1977,1980) = 3914460 / 3
LCM(1977,1980) = 1304820

Properties of LCM 1977 and 1980

(i) The LCM of 1980 and 1977 is associative

LCM of 1977 and 1980 = LCM of 1980 and 1977

Related Least Common Multiples of 1977

Related Least Common Multiples of 1980

Frequently Asked Questions on LCM of 1977 and 1980

1. What is the LCM of 1977 and 1980?

Answer: LCM of 1977 and 1980 is 1304820.

2. What are the Factors of 1977?

Answer: Factors of 1977 are 1, 3, 659, 1977. There are 4 integers that are factors of 1977. The greatest factor of 1977 is 1977.

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 1977 and 1980?

Answer:

Least Common Multiple of 1977 and 1980 = 1304820

Step 1: Find the prime factorization of 1977

1977 = 3 x 659

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 = 1304820 = 2 x 2 x 3 x 3 x 5 x 11 x 659

Step 4: Therefore, the least common multiple of 1977 and 1980 is 1304820.