Least Common Multiple of 74 and 75

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 74 and 75 the smallest integer that is 5550 that is divisible by both numbers.

Least Common Multiple (LCM) of 74 and 75 is 5550.

LCM(74,75) = 5550

LCM of 74 and 75

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

LCM of:
and

Least Common Multiple of 74 and 75

LCM of 74 and 75 is 5550

Least common multiple can be found by multiplying the highest exponent prime factors of 74 and 75. First we will calculate the prime factors of 74 and 75.

Prime Factorization of 74


2 74
37 37
1

Prime factors of 74 are 2,37. Prime factorization of 74 in exponential form is:

74 = 21×371

Prime Factorization of 75


3 75
5 25
5 5
1

Prime factors of 75 are 3,5. Prime factorization of 75 in exponential form is:

75 = 31×52

Now multiplying the highest exponent prime factors to calculate the LCM of 74 and 75.

LCM(74,75) = 21×31×52×371
LCM(74,75) = 5550

Factors of 74

List of positive integer factors of 74 that divides 74 without a remainder.

1, 2, 37, 74

Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1, 3, 5, 15, 25, 75

Least Common Multiple of 74 and 75 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 74 and 75, than apply into the LCM equation.

GCF(74,75) = 1
LCM(74,75) = ( 74 × 75) / 1
LCM(74,75) = 5550 / 1
LCM(74,75) = 5550

Properties of LCM 74 and 75

(i) The LCM of 75 and 74 is associative

LCM of 74 and 75 = LCM of 75 and 74

Related Least Common Multiples of 74

Related Least Common Multiples of 75

Frequently Asked Questions on LCM of 74 and 75

1. What is the LCM of 74 and 75?

Answer: LCM of 74 and 75 is 5550.

2. What are the Factors of 74?

Answer: Factors of 74 are 1, 2, 37, 74. There are 4 integers that are factors of 74. The greatest factor of 74 is 74.

3. What are the Factors of 75?

Answer: Factors of 75 are 1, 3, 5, 15, 25, 75. There are 6 integers that are factors of 75. The greatest factor of 75 is 75.

4. How to Find the LCM of 74 and 75?

Answer:

Least Common Multiple of 74 and 75 = 5550

Step 1: Find the prime factorization of 74

74 = 2 x 37

Step 2: Find the prime factorization of 75

75 = 3 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 = 5550 = 2 x 3 x 5 x 5 x 37

Step 4: Therefore, the least common multiple of 74 and 75 is 5550.