Least Common Multiple of 1980 and 1985

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 1985 the smallest integer that is 786060 that is divisible by both numbers.

Least Common Multiple (LCM) of 1980 and 1985 is 786060.

LCM(1980,1985) = 786060

LCM of 1980 and 1985

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

LCM of:
and

Least Common Multiple of 1980 and 1985

LCM of 1980 and 1985 is 786060

Least common multiple can be found by multiplying the highest exponent prime factors of 1980 and 1985. First we will calculate the prime factors of 1980 and 1985.

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 1985


5 1985
397 397
1

Prime factors of 1985 are 5,397. Prime factorization of 1985 in exponential form is:

1985 = 51×3971

Now multiplying the highest exponent prime factors to calculate the LCM of 1980 and 1985.

LCM(1980,1985) = 22×32×51×111×3971
LCM(1980,1985) = 786060

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 1985

List of positive integer factors of 1985 that divides 1985 without a remainder.

1, 5, 397, 1985

Least Common Multiple of 1980 and 1985 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 1985, than apply into the LCM equation.

GCF(1980,1985) = 5
LCM(1980,1985) = ( 1980 × 1985) / 5
LCM(1980,1985) = 3930300 / 5
LCM(1980,1985) = 786060

Properties of LCM 1980 and 1985

(i) The LCM of 1985 and 1980 is associative

LCM of 1980 and 1985 = LCM of 1985 and 1980

Related Least Common Multiples of 1980

Related Least Common Multiples of 1985

Frequently Asked Questions on LCM of 1980 and 1985

1. What is the LCM of 1980 and 1985?

Answer: LCM of 1980 and 1985 is 786060.

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 1985?

Answer: Factors of 1985 are 1, 5, 397, 1985. There are 4 integers that are factors of 1985. The greatest factor of 1985 is 1985.

4. How to Find the LCM of 1980 and 1985?

Answer:

Least Common Multiple of 1980 and 1985 = 786060

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 1985

1985 = 5 x 397

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

LCM = 786060 = 2 x 2 x 3 x 3 x 5 x 11 x 397

Step 4: Therefore, the least common multiple of 1980 and 1985 is 786060.