Least Common Multiple of 1988 and 1992

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1988 and 1992 the smallest integer that is 990024 that is divisible by both numbers.

Least Common Multiple (LCM) of 1988 and 1992 is 990024.

LCM(1988,1992) = 990024

LCM of 1988 and 1992

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

LCM of:
and

Least Common Multiple of 1988 and 1992

LCM of 1988 and 1992 is 990024

Least common multiple can be found by multiplying the highest exponent prime factors of 1988 and 1992. First we will calculate the prime factors of 1988 and 1992.

Prime Factorization of 1988


2 1988
2 994
7 497
71 71
1

Prime factors of 1988 are 2, 7,71. Prime factorization of 1988 in exponential form is:

1988 = 22×71×711

Prime Factorization of 1992


2 1992
2 996
2 498
3 249
83 83
1

Prime factors of 1992 are 2, 3,83. Prime factorization of 1992 in exponential form is:

1992 = 23×31×831

Now multiplying the highest exponent prime factors to calculate the LCM of 1988 and 1992.

LCM(1988,1992) = 23×31×71×711×831
LCM(1988,1992) = 990024

Factors of 1988

List of positive integer factors of 1988 that divides 1988 without a remainder.

1, 2, 4, 7, 14, 28, 71, 142, 284, 497, 994, 1988

Factors of 1992

List of positive integer factors of 1992 that divides 1992 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 83, 166, 249, 332, 498, 664, 996, 1992

Least Common Multiple of 1988 and 1992 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1988 and 1992, than apply into the LCM equation.

GCF(1988,1992) = 4
LCM(1988,1992) = ( 1988 × 1992) / 4
LCM(1988,1992) = 3960096 / 4
LCM(1988,1992) = 990024

Properties of LCM 1988 and 1992

(i) The LCM of 1992 and 1988 is associative

LCM of 1988 and 1992 = LCM of 1992 and 1988

Related Least Common Multiples of 1988

Related Least Common Multiples of 1992

Frequently Asked Questions on LCM of 1988 and 1992

1. What is the LCM of 1988 and 1992?

Answer: LCM of 1988 and 1992 is 990024.

2. What are the Factors of 1988?

Answer: Factors of 1988 are 1, 2, 4, 7, 14, 28, 71, 142, 284, 497, 994, 1988. There are 12 integers that are factors of 1988. The greatest factor of 1988 is 1988.

3. What are the Factors of 1992?

Answer: Factors of 1992 are 1, 2, 3, 4, 6, 8, 12, 24, 83, 166, 249, 332, 498, 664, 996, 1992. There are 16 integers that are factors of 1992. The greatest factor of 1992 is 1992.

4. How to Find the LCM of 1988 and 1992?

Answer:

Least Common Multiple of 1988 and 1992 = 990024

Step 1: Find the prime factorization of 1988

1988 = 2 x 2 x 7 x 71

Step 2: Find the prime factorization of 1992

1992 = 2 x 2 x 2 x 3 x 83

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

LCM = 990024 = 2 x 2 x 2 x 3 x 7 x 71 x 83

Step 4: Therefore, the least common multiple of 1988 and 1992 is 990024.