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Least Common Multiple of 10 and 17

Free LCM Calculator determines the least common multiple (LCM) between 10 and 17 the smallest integer that is 170 that is divisible by both numbers.

Least Common Multiple (LCM) of 10 and 17 is 170.

LCM(10,17) = 170

LCM of 10 and 17

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

LCM of:
and

Least Common Multiple (LCM) of 10 and 17 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 17. First we will calculate the prime factors of 10 and 17.

Prime Factorization of 10


2 10
5 5
1

Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:

10 = 21×51

Prime Factorization of 17


17 17
1

Prime factors of 17 are 17. Prime factorization of 17 in exponential form is:

17 = 171

Now multiplying the highest exponent prime factors to calculate the LCM of 10 and 17.

LCM(10,17) = 21×51×171
LCM(10,17) = 170

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5, 10

Factors of 17

List of positive integer factors of 17 that divides 17 without a remainder.

1, 17

Least Common Multiple of 10 and 17 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10 and 17, than apply into the LCM equation.

GCF(10,17) = 1
LCM(10,17) = ( 10 × 17) / 1
LCM(10,17) = 170 / 1
LCM(10,17) = 170

Properties of LCM 10 and 17

(i) The LCM of 17 and 10 is associative

LCM of 10 and 17 = LCM of 17 and 10

Frequently Asked Questions on LCM of 10 and 17

1. What is the LCM of 10 and 17?

Answer: LCM of 10 and 17 is 170.

2. What are the Factors of 10?

Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.

3. What are the Factors of 17?

Answer: Factors of 17 are 1, 17. There are 2 integers that are factors of 17. The greatest factor of 17 is 17.

4. How to Find the LCM of 10 and 17?

Answer:

Least Common Multiple of 10 and 17 = 170

Step 1: Find the prime factorization of 10

10 = 2 x 5

Step 2: Find the prime factorization of 17

17 = 17

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

LCM = 170 = 2 x 5 x 17

Step 4: Therefore, the least common multiple of 10 and 17 is 170.