Least Common Multiple of 21507 and 21515

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

• Least Common Multiple of 21507 and 21515 by Prime method
• Least Common Multiple of 21507 and 21515 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 21507 and 21515. First we will calculate the prime factors of 21507 and 21515.

Prime Factorization of 21507

Prime factors of 21507 are 3, 67,107. Prime factorization of 21507 in exponential form is:

21507 = 3¹×67¹×107¹

Prime Factorization of 21515

Prime factors of 21515 are 5, 13,331. Prime factorization of 21515 in exponential form is:

21515 = 5¹×13¹×331¹

Now multiplying the highest exponent prime factors to calculate the LCM of 21507 and 21515.

LCM(21507,21515) = 3¹×5¹×13¹×67¹×107¹×331¹
LCM(21507,21515) = 462723105

Factors of 21507

List of positive integer factors of 21507 that divides 21507 without a remainder.

1, 3, 67, 107, 201, 321, 7169, 21507

Factors of 21515

List of positive integer factors of 21515 that divides 21515 without a remainder.

1, 5, 13, 65, 331, 1655, 4303, 21515

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21507 and 21515, than apply into the LCM equation.

GCF(21507,21515) = 1
LCM(21507,21515) = ( 21507 × 21515) / 1
LCM(21507,21515) = 462723105 / 1
LCM(21507,21515) = 462723105

(i) The LCM of 21515 and 21507 is associative

LCM of 21507 and 21515 = LCM of 21515 and 21507

1. What is the LCM of 21507 and 21515?

Answer: LCM of 21507 and 21515 is 462723105.

2. What are the Factors of 21507?

Answer: Factors of 21507 are 1, 3, 67, 107, 201, 321, 7169, 21507. There are 8 integers that are factors of 21507. The greatest factor of 21507 is 21507.

3. What are the Factors of 21515?

Answer: Factors of 21515 are 1, 5, 13, 65, 331, 1655, 4303, 21515. There are 8 integers that are factors of 21515. The greatest factor of 21515 is 21515.

4. How to Find the LCM of 21507 and 21515?

Answer:

Least Common Multiple of 21507 and 21515 = 462723105

Step 1: Find the prime factorization of 21507

21507 = 3 x 67 x 107

Step 2: Find the prime factorization of 21515

21515 = 5 x 13 x 331

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

LCM = 462723105 = 3 x 5 x 13 x 67 x 107 x 331

Step 4: Therefore, the least common multiple of 21507 and 21515 is 462723105.