Least Common Multiple of 1974 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 1974 and 1980 the smallest integer that is 651420 that is divisible by both numbers.

Least Common Multiple (LCM) of 1974 and 1980 is 651420.

LCM(1974,1980) = 651420

LCM of 1974 and 1980

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

LCM of:
and

Least Common Multiple of 1974 and 1980

LCM of 1974 and 1980 is 651420

Least common multiple can be found by multiplying the highest exponent prime factors of 1974 and 1980. First we will calculate the prime factors of 1974 and 1980.

Prime Factorization of 1974


2 1974
3 987
7 329
47 47
1

Prime factors of 1974 are 2, 3, 7,47. Prime factorization of 1974 in exponential form is:

1974 = 21×31×71×471

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 1974 and 1980.

LCM(1974,1980) = 22×32×51×71×111×471
LCM(1974,1980) = 651420

Factors of 1974

List of positive integer factors of 1974 that divides 1974 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987, 1974

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 1974 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 1974 and 1980, than apply into the LCM equation.

GCF(1974,1980) = 6
LCM(1974,1980) = ( 1974 × 1980) / 6
LCM(1974,1980) = 3908520 / 6
LCM(1974,1980) = 651420

Properties of LCM 1974 and 1980

(i) The LCM of 1980 and 1974 is associative

LCM of 1974 and 1980 = LCM of 1980 and 1974

Related Least Common Multiples of 1974

Related Least Common Multiples of 1980

Frequently Asked Questions on LCM of 1974 and 1980

1. What is the LCM of 1974 and 1980?

Answer: LCM of 1974 and 1980 is 651420.

2. What are the Factors of 1974?

Answer: Factors of 1974 are 1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987, 1974. There are 16 integers that are factors of 1974. The greatest factor of 1974 is 1974.

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 1974 and 1980?

Answer:

Least Common Multiple of 1974 and 1980 = 651420

Step 1: Find the prime factorization of 1974

1974 = 2 x 3 x 7 x 47

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 = 651420 = 2 x 2 x 3 x 3 x 5 x 7 x 11 x 47

Step 4: Therefore, the least common multiple of 1974 and 1980 is 651420.