Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 506 and 508 the smallest integer that is 128524 that is divisible by both numbers.
Least Common Multiple (LCM) of 506 and 508 is 128524.
LCM(506,508) = 128524
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 506 and 508. First we will calculate the prime factors of 506 and 508.
Prime Factorization of 506
2 | 506 |
11 | 253 |
23 | 23 |
1 |
Prime factors of 506 are 2, 11,23. Prime factorization of 506 in exponential form is:
506 = 21×111×231
Prime Factorization of 508
2 | 508 |
2 | 254 |
127 | 127 |
1 |
Prime factors of 508 are 2,127. Prime factorization of 508 in exponential form is:
508 = 22×1271
Now multiplying the highest exponent prime factors to calculate the LCM of 506 and 508.
LCM(506,508) = 22×111×231×1271
LCM(506,508) = 128524
Factors of 506
List of positive integer factors of 506 that divides 506 without a remainder.
1, 2, 11, 22, 23, 46, 253, 506
Factors of 508
List of positive integer factors of 508 that divides 508 without a remainder.
1, 2, 4, 127, 254, 508
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 506 and 508, than apply into the LCM equation.
GCF(506,508) = 2
LCM(506,508) = ( 506 × 508) / 2
LCM(506,508) = 257048 / 2
LCM(506,508) = 128524
(i) The LCM of 508 and 506 is associative
LCM of 506 and 508 = LCM of 508 and 506
1. What is the LCM of 506 and 508?
Answer: LCM of 506 and 508 is 128524.
2. What are the Factors of 506?
Answer: Factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506. There are 8 integers that are factors of 506. The greatest factor of 506 is 506.
3. What are the Factors of 508?
Answer: Factors of 508 are 1, 2, 4, 127, 254, 508. There are 6 integers that are factors of 508. The greatest factor of 508 is 508.
4. How to Find the LCM of 506 and 508?
Answer:
Least Common Multiple of 506 and 508 = 128524
Step 1: Find the prime factorization of 506
506 = 2 x 11 x 23
Step 2: Find the prime factorization of 508
508 = 2 x 2 x 127
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 128524 = 2 x 2 x 11 x 23 x 127
Step 4: Therefore, the least common multiple of 506 and 508 is 128524.