Least Common Multiple of 20405 and 20412

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 20405 and 20412 the smallest integer that is 59500980 that is divisible by both numbers.

Least Common Multiple (LCM) of 20405 and 20412 is 59500980.

LCM(20405,20412) = 59500980

LCM of 20405 and 20412

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

LCM of:
and

Least Common Multiple of 20405 and 20412

LCM of 20405 and 20412 is 59500980

Least common multiple can be found by multiplying the highest exponent prime factors of 20405 and 20412. First we will calculate the prime factors of 20405 and 20412.

Prime Factorization of 20405


5 20405
7 4081
11 583
53 53
1

Prime factors of 20405 are 5, 7, 11,53. Prime factorization of 20405 in exponential form is:

20405 = 51×71×111×531

Prime Factorization of 20412


2 20412
2 10206
3 5103
3 1701
3 567
3 189
3 63
3 21
7 7
1

Prime factors of 20412 are 2, 3,7. Prime factorization of 20412 in exponential form is:

20412 = 22×36×71

Now multiplying the highest exponent prime factors to calculate the LCM of 20405 and 20412.

LCM(20405,20412) = 22×36×51×71×111×531
LCM(20405,20412) = 59500980

Factors of 20405

List of positive integer factors of 20405 that divides 20405 without a remainder.

1, 5, 7, 11, 35, 53, 55, 77, 265, 371, 385, 583, 1855, 2915, 4081, 20405

Factors of 20412

List of positive integer factors of 20412 that divides 20412 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 81, 84, 108, 126, 162, 189, 243, 252, 324, 378, 486, 567, 729, 756, 972, 1134, 1458, 1701, 2268, 2916, 3402, 5103, 6804, 10206, 20412

Least Common Multiple of 20405 and 20412 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20405 and 20412, than apply into the LCM equation.

GCF(20405,20412) = 7
LCM(20405,20412) = ( 20405 × 20412) / 7
LCM(20405,20412) = 416506860 / 7
LCM(20405,20412) = 59500980

Properties of LCM 20405 and 20412

(i) The LCM of 20412 and 20405 is associative

LCM of 20405 and 20412 = LCM of 20412 and 20405

Related Least Common Multiples of 20405

Related Least Common Multiples of 20412

Frequently Asked Questions on LCM of 20405 and 20412

1. What is the LCM of 20405 and 20412?

Answer: LCM of 20405 and 20412 is 59500980.

2. What are the Factors of 20405?

Answer: Factors of 20405 are 1, 5, 7, 11, 35, 53, 55, 77, 265, 371, 385, 583, 1855, 2915, 4081, 20405. There are 16 integers that are factors of 20405. The greatest factor of 20405 is 20405.

3. What are the Factors of 20412?

Answer: Factors of 20412 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 81, 84, 108, 126, 162, 189, 243, 252, 324, 378, 486, 567, 729, 756, 972, 1134, 1458, 1701, 2268, 2916, 3402, 5103, 6804, 10206, 20412. There are 42 integers that are factors of 20412. The greatest factor of 20412 is 20412.

4. How to Find the LCM of 20405 and 20412?

Answer:

Least Common Multiple of 20405 and 20412 = 59500980

Step 1: Find the prime factorization of 20405

20405 = 5 x 7 x 11 x 53

Step 2: Find the prime factorization of 20412

20412 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 7

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

LCM = 59500980 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 5 x 7 x 11 x 53

Step 4: Therefore, the least common multiple of 20405 and 20412 is 59500980.