Least Common Multiple of 3723 and 3731

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

• Least Common Multiple of 3723 and 3731 by Prime method
• Least Common Multiple of 3723 and 3731 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3723 and 3731. First we will calculate the prime factors of 3723 and 3731.

Prime Factorization of 3723

Prime factors of 3723 are 3, 17,73. Prime factorization of 3723 in exponential form is:

3723 = 3¹×17¹×73¹

Prime Factorization of 3731

Prime factors of 3731 are 7, 13,41. Prime factorization of 3731 in exponential form is:

3731 = 7¹×13¹×41¹

Now multiplying the highest exponent prime factors to calculate the LCM of 3723 and 3731.

LCM(3723,3731) = 3¹×7¹×13¹×17¹×41¹×73¹
LCM(3723,3731) = 13890513

Factors of 3723

List of positive integer factors of 3723 that divides 3723 without a remainder.

1, 3, 17, 51, 73, 219, 1241, 3723

Factors of 3731

List of positive integer factors of 3731 that divides 3731 without a remainder.

1, 7, 13, 41, 91, 287, 533, 3731

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3723 and 3731, than apply into the LCM equation.

GCF(3723,3731) = 1
LCM(3723,3731) = ( 3723 × 3731) / 1
LCM(3723,3731) = 13890513 / 1
LCM(3723,3731) = 13890513

(i) The LCM of 3731 and 3723 is associative

LCM of 3723 and 3731 = LCM of 3731 and 3723

1. What is the LCM of 3723 and 3731?

Answer: LCM of 3723 and 3731 is 13890513.

2. What are the Factors of 3723?

Answer: Factors of 3723 are 1, 3, 17, 51, 73, 219, 1241, 3723. There are 8 integers that are factors of 3723. The greatest factor of 3723 is 3723.

3. What are the Factors of 3731?

Answer: Factors of 3731 are 1, 7, 13, 41, 91, 287, 533, 3731. There are 8 integers that are factors of 3731. The greatest factor of 3731 is 3731.

4. How to Find the LCM of 3723 and 3731?

Answer:

Least Common Multiple of 3723 and 3731 = 13890513

Step 1: Find the prime factorization of 3723

3723 = 3 x 17 x 73

Step 2: Find the prime factorization of 3731

3731 = 7 x 13 x 41

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

LCM = 13890513 = 3 x 7 x 13 x 17 x 41 x 73

Step 4: Therefore, the least common multiple of 3723 and 3731 is 13890513.