Least Common Multiple of 1980 and 1984

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 1984 the smallest integer that is 982080 that is divisible by both numbers.

Least Common Multiple (LCM) of 1980 and 1984 is 982080.

LCM(1980,1984) = 982080

LCM of 1980 and 1984

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

LCM of:
and

Least Common Multiple of 1980 and 1984

LCM of 1980 and 1984 is 982080

Least common multiple can be found by multiplying the highest exponent prime factors of 1980 and 1984. First we will calculate the prime factors of 1980 and 1984.

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 1984


2 1984
2 992
2 496
2 248
2 124
2 62
31 31
1

Prime factors of 1984 are 2,31. Prime factorization of 1984 in exponential form is:

1984 = 26×311

Now multiplying the highest exponent prime factors to calculate the LCM of 1980 and 1984.

LCM(1980,1984) = 26×32×51×111×311
LCM(1980,1984) = 982080

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 1984

List of positive integer factors of 1984 that divides 1984 without a remainder.

1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992, 1984

Least Common Multiple of 1980 and 1984 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 1984, than apply into the LCM equation.

GCF(1980,1984) = 4
LCM(1980,1984) = ( 1980 × 1984) / 4
LCM(1980,1984) = 3928320 / 4
LCM(1980,1984) = 982080

Properties of LCM 1980 and 1984

(i) The LCM of 1984 and 1980 is associative

LCM of 1980 and 1984 = LCM of 1984 and 1980

Related Least Common Multiples of 1980

Related Least Common Multiples of 1984

Frequently Asked Questions on LCM of 1980 and 1984

1. What is the LCM of 1980 and 1984?

Answer: LCM of 1980 and 1984 is 982080.

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 1984?

Answer: Factors of 1984 are 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992, 1984. There are 14 integers that are factors of 1984. The greatest factor of 1984 is 1984.

4. How to Find the LCM of 1980 and 1984?

Answer:

Least Common Multiple of 1980 and 1984 = 982080

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 1984

1984 = 2 x 2 x 2 x 2 x 2 x 2 x 31

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

LCM = 982080 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11 x 31

Step 4: Therefore, the least common multiple of 1980 and 1984 is 982080.