Least Common Multiple of 3749 and 3750

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3749 and 3750 the smallest integer that is 14058750 that is divisible by both numbers.

Least Common Multiple (LCM) of 3749 and 3750 is 14058750.

LCM(3749,3750) = 14058750

LCM of 3749 and 3750

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

LCM of:
and

Least Common Multiple of 3749 and 3750

LCM of 3749 and 3750 is 14058750

Least common multiple can be found by multiplying the highest exponent prime factors of 3749 and 3750. First we will calculate the prime factors of 3749 and 3750.

Prime Factorization of 3749


23 3749
163 163
1

Prime factors of 3749 are 23,163. Prime factorization of 3749 in exponential form is:

3749 = 231×1631

Prime Factorization of 3750


2 3750
3 1875
5 625
5 125
5 25
5 5
1

Prime factors of 3750 are 2, 3,5. Prime factorization of 3750 in exponential form is:

3750 = 21×31×54

Now multiplying the highest exponent prime factors to calculate the LCM of 3749 and 3750.

LCM(3749,3750) = 21×31×54×231×1631
LCM(3749,3750) = 14058750

Factors of 3749

List of positive integer factors of 3749 that divides 3749 without a remainder.

1, 23, 163, 3749

Factors of 3750

List of positive integer factors of 3750 that divides 3750 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750

Least Common Multiple of 3749 and 3750 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3749 and 3750, than apply into the LCM equation.

GCF(3749,3750) = 1
LCM(3749,3750) = ( 3749 × 3750) / 1
LCM(3749,3750) = 14058750 / 1
LCM(3749,3750) = 14058750

Properties of LCM 3749 and 3750

(i) The LCM of 3750 and 3749 is associative

LCM of 3749 and 3750 = LCM of 3750 and 3749

Related Least Common Multiples of 3749

Related Least Common Multiples of 3750

Frequently Asked Questions on LCM of 3749 and 3750

1. What is the LCM of 3749 and 3750?

Answer: LCM of 3749 and 3750 is 14058750.

2. What are the Factors of 3749?

Answer: Factors of 3749 are 1, 23, 163, 3749. There are 4 integers that are factors of 3749. The greatest factor of 3749 is 3749.

3. What are the Factors of 3750?

Answer: Factors of 3750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750. There are 20 integers that are factors of 3750. The greatest factor of 3750 is 3750.

4. How to Find the LCM of 3749 and 3750?

Answer:

Least Common Multiple of 3749 and 3750 = 14058750

Step 1: Find the prime factorization of 3749

3749 = 23 x 163

Step 2: Find the prime factorization of 3750

3750 = 2 x 3 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 = 14058750 = 2 x 3 x 5 x 5 x 5 x 5 x 23 x 163

Step 4: Therefore, the least common multiple of 3749 and 3750 is 14058750.