Least Common Multiple of 315414 and 315420

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

• Least Common Multiple of 315414 and 315420 by Prime method
• Least Common Multiple of 315414 and 315420 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 315414 and 315420. First we will calculate the prime factors of 315414 and 315420.

Prime Factorization of 315414

Prime factors of 315414 are 2, 3, 11,59. Prime factorization of 315414 in exponential form is:

315414 = 2¹×3⁵×11¹×59¹

Prime Factorization of 315420

Prime factors of 315420 are 2, 3, 5, 7,751. Prime factorization of 315420 in exponential form is:

315420 = 2²×3¹×5¹×7¹×751¹

Now multiplying the highest exponent prime factors to calculate the LCM of 315414 and 315420.

LCM(315414,315420) = 2²×3⁵×5¹×7¹×11¹×59¹×751¹
LCM(315414,315420) = 16581313980

Factors of 315414

List of positive integer factors of 315414 that divides 315414 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 59, 66, 81, 99, 118, 162, 177, 198, 243, 297, 354, 486, 531, 594, 649, 891, 1062, 1298, 1593, 1782, 1947, 2673, 3186, 3894, 4779, 5346, 5841, 9558, 11682, 14337, 17523, 28674, 35046, 52569, 105138, 157707, 315414

Factors of 315420

List of positive integer factors of 315420 that divides 315420 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420, 751, 1502, 2253, 3004, 3755, 4506, 5257, 7510, 9012, 10514, 11265, 15020, 15771, 21028, 22530, 26285, 31542, 45060, 52570, 63084, 78855, 105140, 157710, 315420

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 315414 and 315420, than apply into the LCM equation.

GCF(315414,315420) = 6
LCM(315414,315420) = ( 315414 × 315420) / 6
LCM(315414,315420) = 99487883880 / 6
LCM(315414,315420) = 16581313980

(i) The LCM of 315420 and 315414 is associative

LCM of 315414 and 315420 = LCM of 315420 and 315414

1. What is the LCM of 315414 and 315420?

Answer: LCM of 315414 and 315420 is 16581313980.

2. What are the Factors of 315414?

Answer: Factors of 315414 are 1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 59, 66, 81, 99, 118, 162, 177, 198, 243, 297, 354, 486, 531, 594, 649, 891, 1062, 1298, 1593, 1782, 1947, 2673, 3186, 3894, 4779, 5346, 5841, 9558, 11682, 14337, 17523, 28674, 35046, 52569, 105138, 157707, 315414. There are 48 integers that are factors of 315414. The greatest factor of 315414 is 315414.

3. What are the Factors of 315420?

Answer: Factors of 315420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420, 751, 1502, 2253, 3004, 3755, 4506, 5257, 7510, 9012, 10514, 11265, 15020, 15771, 21028, 22530, 26285, 31542, 45060, 52570, 63084, 78855, 105140, 157710, 315420. There are 48 integers that are factors of 315420. The greatest factor of 315420 is 315420.

4. How to Find the LCM of 315414 and 315420?

Answer:

Least Common Multiple of 315414 and 315420 = 16581313980

Step 1: Find the prime factorization of 315414

315414 = 2 x 3 x 3 x 3 x 3 x 3 x 11 x 59

Step 2: Find the prime factorization of 315420

315420 = 2 x 2 x 3 x 5 x 7 x 751

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

LCM = 16581313980 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 7 x 11 x 59 x 751

Step 4: Therefore, the least common multiple of 315414 and 315420 is 16581313980.