Least Common Multiple of 12405 and 12410

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

• Least Common Multiple of 12405 and 12410 by Prime method
• Least Common Multiple of 12405 and 12410 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 12405 and 12410. First we will calculate the prime factors of 12405 and 12410.

Prime Factorization of 12405

Prime factors of 12405 are 3, 5,827. Prime factorization of 12405 in exponential form is:

12405 = 3¹×5¹×827¹

Prime Factorization of 12410

Prime factors of 12410 are 2, 5, 17,73. Prime factorization of 12410 in exponential form is:

12410 = 2¹×5¹×17¹×73¹

Now multiplying the highest exponent prime factors to calculate the LCM of 12405 and 12410.

LCM(12405,12410) = 2¹×3¹×5¹×17¹×73¹×827¹
LCM(12405,12410) = 30789210

Factors of 12405

List of positive integer factors of 12405 that divides 12405 without a remainder.

1, 3, 5, 15, 827, 2481, 4135, 12405

Factors of 12410

List of positive integer factors of 12410 that divides 12410 without a remainder.

1, 2, 5, 10, 17, 34, 73, 85, 146, 170, 365, 730, 1241, 2482, 6205, 12410

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12405 and 12410, than apply into the LCM equation.

GCF(12405,12410) = 5
LCM(12405,12410) = ( 12405 × 12410) / 5
LCM(12405,12410) = 153946050 / 5
LCM(12405,12410) = 30789210

(i) The LCM of 12410 and 12405 is associative

LCM of 12405 and 12410 = LCM of 12410 and 12405

1. What is the LCM of 12405 and 12410?

Answer: LCM of 12405 and 12410 is 30789210.

2. What are the Factors of 12405?

Answer: Factors of 12405 are 1, 3, 5, 15, 827, 2481, 4135, 12405. There are 8 integers that are factors of 12405. The greatest factor of 12405 is 12405.

3. What are the Factors of 12410?

Answer: Factors of 12410 are 1, 2, 5, 10, 17, 34, 73, 85, 146, 170, 365, 730, 1241, 2482, 6205, 12410. There are 16 integers that are factors of 12410. The greatest factor of 12410 is 12410.

4. How to Find the LCM of 12405 and 12410?

Answer:

Least Common Multiple of 12405 and 12410 = 30789210

Step 1: Find the prime factorization of 12405

12405 = 3 x 5 x 827

Step 2: Find the prime factorization of 12410

12410 = 2 x 5 x 17 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 = 30789210 = 2 x 3 x 5 x 17 x 73 x 827

Step 4: Therefore, the least common multiple of 12405 and 12410 is 30789210.