Least Common Multiple of 4992 and 5000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 4992 and 5000 the smallest integer that is 3120000 that is divisible by both numbers.

Least Common Multiple (LCM) of 4992 and 5000 is 3120000.

LCM(4992,5000) = 3120000

LCM of 4992 and 5000

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

LCM of:
and

Least Common Multiple of 4992 and 5000

LCM of 4992 and 5000 is 3120000

Least common multiple can be found by multiplying the highest exponent prime factors of 4992 and 5000. First we will calculate the prime factors of 4992 and 5000.

Prime Factorization of 4992


2 4992
2 2496
2 1248
2 624
2 312
2 156
2 78
3 39
13 13
1

Prime factors of 4992 are 2, 3,13. Prime factorization of 4992 in exponential form is:

4992 = 27×31×131

Prime Factorization of 5000


2 5000
2 2500
2 1250
5 625
5 125
5 25
5 5
1

Prime factors of 5000 are 2,5. Prime factorization of 5000 in exponential form is:

5000 = 23×54

Now multiplying the highest exponent prime factors to calculate the LCM of 4992 and 5000.

LCM(4992,5000) = 27×31×54×131
LCM(4992,5000) = 3120000

Factors of 4992

List of positive integer factors of 4992 that divides 4992 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 312, 384, 416, 624, 832, 1248, 1664, 2496, 4992

Factors of 5000

List of positive integer factors of 5000 that divides 5000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500, 5000

Least Common Multiple of 4992 and 5000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4992 and 5000, than apply into the LCM equation.

GCF(4992,5000) = 8
LCM(4992,5000) = ( 4992 × 5000) / 8
LCM(4992,5000) = 24960000 / 8
LCM(4992,5000) = 3120000

Properties of LCM 4992 and 5000

(i) The LCM of 5000 and 4992 is associative

LCM of 4992 and 5000 = LCM of 5000 and 4992

Related Least Common Multiples of 4992

Related Least Common Multiples of 5000

Frequently Asked Questions on LCM of 4992 and 5000

1. What is the LCM of 4992 and 5000?

Answer: LCM of 4992 and 5000 is 3120000.

2. What are the Factors of 4992?

Answer: Factors of 4992 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 312, 384, 416, 624, 832, 1248, 1664, 2496, 4992. There are 32 integers that are factors of 4992. The greatest factor of 4992 is 4992.

3. What are the Factors of 5000?

Answer: Factors of 5000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500, 5000. There are 20 integers that are factors of 5000. The greatest factor of 5000 is 5000.

4. How to Find the LCM of 4992 and 5000?

Answer:

Least Common Multiple of 4992 and 5000 = 3120000

Step 1: Find the prime factorization of 4992

4992 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13

Step 2: Find the prime factorization of 5000

5000 = 2 x 2 x 2 x 5 x 5 x 5 x 5

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

LCM = 3120000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 5 x 13

Step 4: Therefore, the least common multiple of 4992 and 5000 is 3120000.