Least Common Multiple of 312402 and 312409

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

• Least Common Multiple of 312402 and 312409 by Prime method
• Least Common Multiple of 312402 and 312409 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 312402 and 312409. First we will calculate the prime factors of 312402 and 312409.

Prime Factorization of 312402

Prime factors of 312402 are 2, 3,52067. Prime factorization of 312402 in exponential form is:

312402 = 2¹×3¹×52067¹

Prime Factorization of 312409

Prime factors of 312409 are 17, 23,47. Prime factorization of 312409 in exponential form is:

312409 = 17²×23¹×47¹

Now multiplying the highest exponent prime factors to calculate the LCM of 312402 and 312409.

LCM(312402,312409) = 2¹×3¹×17²×23¹×47¹×52067¹
LCM(312402,312409) = 97597196418

Factors of 312402

List of positive integer factors of 312402 that divides 312402 without a remainder.

1, 2, 3, 6, 52067, 104134, 156201, 312402

Factors of 312409

List of positive integer factors of 312409 that divides 312409 without a remainder.

1, 17, 23, 47, 289, 391, 799, 1081, 6647, 13583, 18377, 312409

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 312402 and 312409, than apply into the LCM equation.

GCF(312402,312409) = 1
LCM(312402,312409) = ( 312402 × 312409) / 1
LCM(312402,312409) = 97597196418 / 1
LCM(312402,312409) = 97597196418

(i) The LCM of 312409 and 312402 is associative

LCM of 312402 and 312409 = LCM of 312409 and 312402

1. What is the LCM of 312402 and 312409?

Answer: LCM of 312402 and 312409 is 97597196418.

2. What are the Factors of 312402?

Answer: Factors of 312402 are 1, 2, 3, 6, 52067, 104134, 156201, 312402. There are 8 integers that are factors of 312402. The greatest factor of 312402 is 312402.

3. What are the Factors of 312409?

Answer: Factors of 312409 are 1, 17, 23, 47, 289, 391, 799, 1081, 6647, 13583, 18377, 312409. There are 12 integers that are factors of 312409. The greatest factor of 312409 is 312409.

4. How to Find the LCM of 312402 and 312409?

Answer:

Least Common Multiple of 312402 and 312409 = 97597196418

Step 1: Find the prime factorization of 312402

312402 = 2 x 3 x 52067

Step 2: Find the prime factorization of 312409

312409 = 17 x 17 x 23 x 47

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

LCM = 97597196418 = 2 x 3 x 17 x 17 x 23 x 47 x 52067

Step 4: Therefore, the least common multiple of 312402 and 312409 is 97597196418.