Least Common Multiple of 321414 and 321419

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

• Least Common Multiple of 321414 and 321419 by Prime method
• Least Common Multiple of 321414 and 321419 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 321414 and 321419. First we will calculate the prime factors of 321414 and 321419.

Prime Factorization of 321414

Prime factors of 321414 are 2, 3,53569. Prime factorization of 321414 in exponential form is:

321414 = 2¹×3¹×53569¹

Prime Factorization of 321419

Prime factors of 321419 are 7, 17, 37,73. Prime factorization of 321419 in exponential form is:

321419 = 7¹×17¹×37¹×73¹

Now multiplying the highest exponent prime factors to calculate the LCM of 321414 and 321419.

LCM(321414,321419) = 2¹×3¹×7¹×17¹×37¹×73¹×53569¹
LCM(321414,321419) = 103308566466

Factors of 321414

List of positive integer factors of 321414 that divides 321414 without a remainder.

1, 2, 3, 6, 53569, 107138, 160707, 321414

Factors of 321419

List of positive integer factors of 321419 that divides 321419 without a remainder.

1, 7, 17, 37, 73, 119, 259, 511, 629, 1241, 2701, 4403, 8687, 18907, 45917, 321419

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 321414 and 321419, than apply into the LCM equation.

GCF(321414,321419) = 1
LCM(321414,321419) = ( 321414 × 321419) / 1
LCM(321414,321419) = 103308566466 / 1
LCM(321414,321419) = 103308566466

(i) The LCM of 321419 and 321414 is associative

LCM of 321414 and 321419 = LCM of 321419 and 321414

1. What is the LCM of 321414 and 321419?

Answer: LCM of 321414 and 321419 is 103308566466.

2. What are the Factors of 321414?

Answer: Factors of 321414 are 1, 2, 3, 6, 53569, 107138, 160707, 321414. There are 8 integers that are factors of 321414. The greatest factor of 321414 is 321414.

3. What are the Factors of 321419?

Answer: Factors of 321419 are 1, 7, 17, 37, 73, 119, 259, 511, 629, 1241, 2701, 4403, 8687, 18907, 45917, 321419. There are 16 integers that are factors of 321419. The greatest factor of 321419 is 321419.

4. How to Find the LCM of 321414 and 321419?

Answer:

Least Common Multiple of 321414 and 321419 = 103308566466

Step 1: Find the prime factorization of 321414

321414 = 2 x 3 x 53569

Step 2: Find the prime factorization of 321419

321419 = 7 x 17 x 37 x 73

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

LCM = 103308566466 = 2 x 3 x 7 x 17 x 37 x 73 x 53569

Step 4: Therefore, the least common multiple of 321414 and 321419 is 103308566466.