Least Common Multiple of 505 and 510

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 505 and 510 the smallest integer that is 51510 that is divisible by both numbers.

Least Common Multiple (LCM) of 505 and 510 is 51510.

LCM(505,510) = 51510

LCM of 505 and 510

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

LCM of:
and

Least Common Multiple of 505 and 510

LCM of 505 and 510 is 51510

Least common multiple can be found by multiplying the highest exponent prime factors of 505 and 510. First we will calculate the prime factors of 505 and 510.

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

Prime Factorization of 510


2 510
3 255
5 85
17 17
1

Prime factors of 510 are 2, 3, 5,17. Prime factorization of 510 in exponential form is:

510 = 21×31×51×171

Now multiplying the highest exponent prime factors to calculate the LCM of 505 and 510.

LCM(505,510) = 21×31×51×171×1011
LCM(505,510) = 51510

Factors of 505

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

1, 5, 101, 505

Factors of 510

List of positive integer factors of 510 that divides 510 without a remainder.

1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510

Least Common Multiple of 505 and 510 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 505 and 510, than apply into the LCM equation.

GCF(505,510) = 5
LCM(505,510) = ( 505 × 510) / 5
LCM(505,510) = 257550 / 5
LCM(505,510) = 51510

Properties of LCM 505 and 510

(i) The LCM of 510 and 505 is associative

LCM of 505 and 510 = LCM of 510 and 505

Related Least Common Multiples of 505

Related Least Common Multiples of 510

Frequently Asked Questions on LCM of 505 and 510

1. What is the LCM of 505 and 510?

Answer: LCM of 505 and 510 is 51510.

2. 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.

3. What are the Factors of 510?

Answer: Factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510. There are 16 integers that are factors of 510. The greatest factor of 510 is 510.

4. How to Find the LCM of 505 and 510?

Answer:

Least Common Multiple of 505 and 510 = 51510

Step 1: Find the prime factorization of 505

505 = 5 x 101

Step 2: Find the prime factorization of 510

510 = 2 x 3 x 5 x 17

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

LCM = 51510 = 2 x 3 x 5 x 17 x 101

Step 4: Therefore, the least common multiple of 505 and 510 is 51510.