Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2408 and 2412 the smallest integer that is 1452024 that is divisible by both numbers.
Least Common Multiple (LCM) of 2408 and 2412 is 1452024.
LCM(2408,2412) = 1452024
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 2408 and 2412. First we will calculate the prime factors of 2408 and 2412.
Prime Factorization of 2408
2 | 2408 |
2 | 1204 |
2 | 602 |
7 | 301 |
43 | 43 |
1 |
Prime factors of 2408 are 2, 7,43. Prime factorization of 2408 in exponential form is:
2408 = 23×71×431
Prime Factorization of 2412
2 | 2412 |
2 | 1206 |
3 | 603 |
3 | 201 |
67 | 67 |
1 |
Prime factors of 2412 are 2, 3,67. Prime factorization of 2412 in exponential form is:
2412 = 22×32×671
Now multiplying the highest exponent prime factors to calculate the LCM of 2408 and 2412.
LCM(2408,2412) = 23×32×71×431×671
LCM(2408,2412) = 1452024
Factors of 2408
List of positive integer factors of 2408 that divides 2408 without a remainder.
1, 2, 4, 7, 8, 14, 28, 43, 56, 86, 172, 301, 344, 602, 1204, 2408
Factors of 2412
List of positive integer factors of 2412 that divides 2412 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 36, 67, 134, 201, 268, 402, 603, 804, 1206, 2412
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2408 and 2412, than apply into the LCM equation.
GCF(2408,2412) = 4
LCM(2408,2412) = ( 2408 × 2412) / 4
LCM(2408,2412) = 5808096 / 4
LCM(2408,2412) = 1452024
(i) The LCM of 2412 and 2408 is associative
LCM of 2408 and 2412 = LCM of 2412 and 2408
1. What is the LCM of 2408 and 2412?
Answer: LCM of 2408 and 2412 is 1452024.
2. What are the Factors of 2408?
Answer: Factors of 2408 are 1, 2, 4, 7, 8, 14, 28, 43, 56, 86, 172, 301, 344, 602, 1204, 2408. There are 16 integers that are factors of 2408. The greatest factor of 2408 is 2408.
3. What are the Factors of 2412?
Answer: Factors of 2412 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 67, 134, 201, 268, 402, 603, 804, 1206, 2412. There are 18 integers that are factors of 2412. The greatest factor of 2412 is 2412.
4. How to Find the LCM of 2408 and 2412?
Answer:
Least Common Multiple of 2408 and 2412 = 1452024
Step 1: Find the prime factorization of 2408
2408 = 2 x 2 x 2 x 7 x 43
Step 2: Find the prime factorization of 2412
2412 = 2 x 2 x 3 x 3 x 67
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1452024 = 2 x 2 x 2 x 3 x 3 x 7 x 43 x 67
Step 4: Therefore, the least common multiple of 2408 and 2412 is 1452024.