Least Common Multiple of 3968 and 3975

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3968 and 3975 the smallest integer that is 15772800 that is divisible by both numbers.

Least Common Multiple (LCM) of 3968 and 3975 is 15772800.

LCM(3968,3975) = 15772800

LCM of 3968 and 3975

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

LCM of:
and

Least Common Multiple of 3968 and 3975

LCM of 3968 and 3975 is 15772800

Least common multiple can be found by multiplying the highest exponent prime factors of 3968 and 3975. First we will calculate the prime factors of 3968 and 3975.

Prime Factorization of 3968


2 3968
2 1984
2 992
2 496
2 248
2 124
2 62
31 31
1

Prime factors of 3968 are 2,31. Prime factorization of 3968 in exponential form is:

3968 = 27×311

Prime Factorization of 3975


3 3975
5 1325
5 265
53 53
1

Prime factors of 3975 are 3, 5,53. Prime factorization of 3975 in exponential form is:

3975 = 31×52×531

Now multiplying the highest exponent prime factors to calculate the LCM of 3968 and 3975.

LCM(3968,3975) = 27×31×52×311×531
LCM(3968,3975) = 15772800

Factors of 3968

List of positive integer factors of 3968 that divides 3968 without a remainder.

1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 128, 248, 496, 992, 1984, 3968

Factors of 3975

List of positive integer factors of 3975 that divides 3975 without a remainder.

1, 3, 5, 15, 25, 53, 75, 159, 265, 795, 1325, 3975

Least Common Multiple of 3968 and 3975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3968 and 3975, than apply into the LCM equation.

GCF(3968,3975) = 1
LCM(3968,3975) = ( 3968 × 3975) / 1
LCM(3968,3975) = 15772800 / 1
LCM(3968,3975) = 15772800

Properties of LCM 3968 and 3975

(i) The LCM of 3975 and 3968 is associative

LCM of 3968 and 3975 = LCM of 3975 and 3968

Related Least Common Multiples of 3968

Related Least Common Multiples of 3975

Frequently Asked Questions on LCM of 3968 and 3975

1. What is the LCM of 3968 and 3975?

Answer: LCM of 3968 and 3975 is 15772800.

2. What are the Factors of 3968?

Answer: Factors of 3968 are 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 128, 248, 496, 992, 1984, 3968. There are 16 integers that are factors of 3968. The greatest factor of 3968 is 3968.

3. What are the Factors of 3975?

Answer: Factors of 3975 are 1, 3, 5, 15, 25, 53, 75, 159, 265, 795, 1325, 3975. There are 12 integers that are factors of 3975. The greatest factor of 3975 is 3975.

4. How to Find the LCM of 3968 and 3975?

Answer:

Least Common Multiple of 3968 and 3975 = 15772800

Step 1: Find the prime factorization of 3968

3968 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 31

Step 2: Find the prime factorization of 3975

3975 = 3 x 5 x 5 x 53

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

LCM = 15772800 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 31 x 53

Step 4: Therefore, the least common multiple of 3968 and 3975 is 15772800.