Least Common Multiple of 410 and 417

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 410 and 417 the smallest integer that is 170970 that is divisible by both numbers.

Least Common Multiple (LCM) of 410 and 417 is 170970.

LCM(410,417) = 170970

LCM of 410 and 417

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

LCM of:
and

Least Common Multiple of 410 and 417

LCM of 410 and 417 is 170970

Least common multiple can be found by multiplying the highest exponent prime factors of 410 and 417. First we will calculate the prime factors of 410 and 417.

Prime Factorization of 410


2 410
5 205
41 41
1

Prime factors of 410 are 2, 5,41. Prime factorization of 410 in exponential form is:

410 = 21×51×411

Prime Factorization of 417


3 417
139 139
1

Prime factors of 417 are 3,139. Prime factorization of 417 in exponential form is:

417 = 31×1391

Now multiplying the highest exponent prime factors to calculate the LCM of 410 and 417.

LCM(410,417) = 21×31×51×411×1391
LCM(410,417) = 170970

Factors of 410

List of positive integer factors of 410 that divides 410 without a remainder.

1, 2, 5, 10, 41, 82, 205, 410

Factors of 417

List of positive integer factors of 417 that divides 417 without a remainder.

1, 3, 139, 417

Least Common Multiple of 410 and 417 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 410 and 417, than apply into the LCM equation.

GCF(410,417) = 1
LCM(410,417) = ( 410 × 417) / 1
LCM(410,417) = 170970 / 1
LCM(410,417) = 170970

Properties of LCM 410 and 417

(i) The LCM of 417 and 410 is associative

LCM of 410 and 417 = LCM of 417 and 410

Related Least Common Multiples of 410

Related Least Common Multiples of 417

Frequently Asked Questions on LCM of 410 and 417

1. What is the LCM of 410 and 417?

Answer: LCM of 410 and 417 is 170970.

2. What are the Factors of 410?

Answer: Factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410. There are 8 integers that are factors of 410. The greatest factor of 410 is 410.

3. What are the Factors of 417?

Answer: Factors of 417 are 1, 3, 139, 417. There are 4 integers that are factors of 417. The greatest factor of 417 is 417.

4. How to Find the LCM of 410 and 417?

Answer:

Least Common Multiple of 410 and 417 = 170970

Step 1: Find the prime factorization of 410

410 = 2 x 5 x 41

Step 2: Find the prime factorization of 417

417 = 3 x 139

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

LCM = 170970 = 2 x 3 x 5 x 41 x 139

Step 4: Therefore, the least common multiple of 410 and 417 is 170970.