Least Common Multiple of 504 and 505

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 504 and 505 the smallest integer that is 254520 that is divisible by both numbers.

Least Common Multiple (LCM) of 504 and 505 is 254520.

LCM(504,505) = 254520

LCM of 504 and 505

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

LCM of:
and

Least Common Multiple of 504 and 505

LCM of 504 and 505 is 254520

Least common multiple can be found by multiplying the highest exponent prime factors of 504 and 505. First we will calculate the prime factors of 504 and 505.

Prime Factorization of 504


2 504
2 252
2 126
3 63
3 21
7 7
1

Prime factors of 504 are 2, 3,7. Prime factorization of 504 in exponential form is:

504 = 23×32×71

Prime Factorization of 505


5 505
101 101
1

Prime factors of 505 are 5,101. Prime factorization of 505 in exponential form is:

505 = 51×1011

Now multiplying the highest exponent prime factors to calculate the LCM of 504 and 505.

LCM(504,505) = 23×32×51×71×1011
LCM(504,505) = 254520

Factors of 504

List of positive integer factors of 504 that divides 504 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504

Factors of 505

List of positive integer factors of 505 that divides 505 without a remainder.

1, 5, 101, 505

Least Common Multiple of 504 and 505 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 504 and 505, than apply into the LCM equation.

GCF(504,505) = 1
LCM(504,505) = ( 504 × 505) / 1
LCM(504,505) = 254520 / 1
LCM(504,505) = 254520

Properties of LCM 504 and 505

(i) The LCM of 505 and 504 is associative

LCM of 504 and 505 = LCM of 505 and 504

Related Least Common Multiples of 504

Related Least Common Multiples of 505

Frequently Asked Questions on LCM of 504 and 505

1. What is the LCM of 504 and 505?

Answer: LCM of 504 and 505 is 254520.

2. What are the Factors of 504?

Answer: Factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504. There are 24 integers that are factors of 504. The greatest factor of 504 is 504.

3. What are the Factors of 505?

Answer: Factors of 505 are 1, 5, 101, 505. There are 4 integers that are factors of 505. The greatest factor of 505 is 505.

4. How to Find the LCM of 504 and 505?

Answer:

Least Common Multiple of 504 and 505 = 254520

Step 1: Find the prime factorization of 504

504 = 2 x 2 x 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 505

505 = 5 x 101

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

LCM = 254520 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 101

Step 4: Therefore, the least common multiple of 504 and 505 is 254520.