Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 520 and 525 the smallest integer that is 54600 that is divisible by both numbers.
Least Common Multiple (LCM) of 520 and 525 is 54600.
LCM(520,525) = 54600
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 520 and 525. First we will calculate the prime factors of 520 and 525.
Prime Factorization of 520
2 | 520 |
2 | 260 |
2 | 130 |
5 | 65 |
13 | 13 |
1 |
Prime factors of 520 are 2, 5,13. Prime factorization of 520 in exponential form is:
520 = 23×51×131
Prime Factorization of 525
3 | 525 |
5 | 175 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 525 are 3, 5,7. Prime factorization of 525 in exponential form is:
525 = 31×52×71
Now multiplying the highest exponent prime factors to calculate the LCM of 520 and 525.
LCM(520,525) = 23×31×52×71×131
LCM(520,525) = 54600
Factors of 520
List of positive integer factors of 520 that divides 520 without a remainder.
1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
Factors of 525
List of positive integer factors of 525 that divides 525 without a remainder.
1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 520 and 525, than apply into the LCM equation.
GCF(520,525) = 5
LCM(520,525) = ( 520 × 525) / 5
LCM(520,525) = 273000 / 5
LCM(520,525) = 54600
(i) The LCM of 525 and 520 is associative
LCM of 520 and 525 = LCM of 525 and 520
1. What is the LCM of 520 and 525?
Answer: LCM of 520 and 525 is 54600.
2. What are the Factors of 520?
Answer: Factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520. There are 16 integers that are factors of 520. The greatest factor of 520 is 520.
3. What are the Factors of 525?
Answer: Factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525. There are 12 integers that are factors of 525. The greatest factor of 525 is 525.
4. How to Find the LCM of 520 and 525?
Answer:
Least Common Multiple of 520 and 525 = 54600
Step 1: Find the prime factorization of 520
520 = 2 x 2 x 2 x 5 x 13
Step 2: Find the prime factorization of 525
525 = 3 x 5 x 5 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 = 54600 = 2 x 2 x 2 x 3 x 5 x 5 x 7 x 13
Step 4: Therefore, the least common multiple of 520 and 525 is 54600.