Least Common Multiple of 15314 and 15315

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

• Least Common Multiple of 15314 and 15315 by Prime method
• Least Common Multiple of 15314 and 15315 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 15314 and 15315. First we will calculate the prime factors of 15314 and 15315.

Prime Factorization of 15314

Prime factors of 15314 are 2, 13, 19,31. Prime factorization of 15314 in exponential form is:

15314 = 2¹×13¹×19¹×31¹

Prime Factorization of 15315

Prime factors of 15315 are 3, 5,1021. Prime factorization of 15315 in exponential form is:

15315 = 3¹×5¹×1021¹

Now multiplying the highest exponent prime factors to calculate the LCM of 15314 and 15315.

LCM(15314,15315) = 2¹×3¹×5¹×13¹×19¹×31¹×1021¹
LCM(15314,15315) = 234533910

Factors of 15314

List of positive integer factors of 15314 that divides 15314 without a remainder.

1, 2, 13, 19, 26, 31, 38, 62, 247, 403, 494, 589, 806, 1178, 7657, 15314

Factors of 15315

List of positive integer factors of 15315 that divides 15315 without a remainder.

1, 3, 5, 15, 1021, 3063, 5105, 15315

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15314 and 15315, than apply into the LCM equation.

GCF(15314,15315) = 1
LCM(15314,15315) = ( 15314 × 15315) / 1
LCM(15314,15315) = 234533910 / 1
LCM(15314,15315) = 234533910

(i) The LCM of 15315 and 15314 is associative

LCM of 15314 and 15315 = LCM of 15315 and 15314

1. What is the LCM of 15314 and 15315?

Answer: LCM of 15314 and 15315 is 234533910.

2. What are the Factors of 15314?

Answer: Factors of 15314 are 1, 2, 13, 19, 26, 31, 38, 62, 247, 403, 494, 589, 806, 1178, 7657, 15314. There are 16 integers that are factors of 15314. The greatest factor of 15314 is 15314.

3. What are the Factors of 15315?

Answer: Factors of 15315 are 1, 3, 5, 15, 1021, 3063, 5105, 15315. There are 8 integers that are factors of 15315. The greatest factor of 15315 is 15315.

4. How to Find the LCM of 15314 and 15315?

Answer:

Least Common Multiple of 15314 and 15315 = 234533910

Step 1: Find the prime factorization of 15314

15314 = 2 x 13 x 19 x 31

Step 2: Find the prime factorization of 15315

15315 = 3 x 5 x 1021

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

LCM = 234533910 = 2 x 3 x 5 x 13 x 19 x 31 x 1021

Step 4: Therefore, the least common multiple of 15314 and 15315 is 234533910.