Least Common Multiple of 1700 and 1708

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1700 and 1708 the smallest integer that is 725900 that is divisible by both numbers.

Least Common Multiple (LCM) of 1700 and 1708 is 725900.

LCM(1700,1708) = 725900

LCM of 1700 and 1708

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

LCM of:
and

Least Common Multiple of 1700 and 1708

LCM of 1700 and 1708 is 725900

Least common multiple can be found by multiplying the highest exponent prime factors of 1700 and 1708. First we will calculate the prime factors of 1700 and 1708.

Prime Factorization of 1700


2 1700
2 850
5 425
5 85
17 17
1

Prime factors of 1700 are 2, 5,17. Prime factorization of 1700 in exponential form is:

1700 = 22×52×171

Prime Factorization of 1708


2 1708
2 854
7 427
61 61
1

Prime factors of 1708 are 2, 7,61. Prime factorization of 1708 in exponential form is:

1708 = 22×71×611

Now multiplying the highest exponent prime factors to calculate the LCM of 1700 and 1708.

LCM(1700,1708) = 22×52×71×171×611
LCM(1700,1708) = 725900

Factors of 1700

List of positive integer factors of 1700 that divides 1700 without a remainder.

1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, 1700

Factors of 1708

List of positive integer factors of 1708 that divides 1708 without a remainder.

1, 2, 4, 7, 14, 28, 61, 122, 244, 427, 854, 1708

Least Common Multiple of 1700 and 1708 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1700 and 1708, than apply into the LCM equation.

GCF(1700,1708) = 4
LCM(1700,1708) = ( 1700 × 1708) / 4
LCM(1700,1708) = 2903600 / 4
LCM(1700,1708) = 725900

Properties of LCM 1700 and 1708

(i) The LCM of 1708 and 1700 is associative

LCM of 1700 and 1708 = LCM of 1708 and 1700

Related Least Common Multiples of 1700

Related Least Common Multiples of 1708

Frequently Asked Questions on LCM of 1700 and 1708

1. What is the LCM of 1700 and 1708?

Answer: LCM of 1700 and 1708 is 725900.

2. What are the Factors of 1700?

Answer: Factors of 1700 are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, 1700. There are 18 integers that are factors of 1700. The greatest factor of 1700 is 1700.

3. What are the Factors of 1708?

Answer: Factors of 1708 are 1, 2, 4, 7, 14, 28, 61, 122, 244, 427, 854, 1708. There are 12 integers that are factors of 1708. The greatest factor of 1708 is 1708.

4. How to Find the LCM of 1700 and 1708?

Answer:

Least Common Multiple of 1700 and 1708 = 725900

Step 1: Find the prime factorization of 1700

1700 = 2 x 2 x 5 x 5 x 17

Step 2: Find the prime factorization of 1708

1708 = 2 x 2 x 7 x 61

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

LCM = 725900 = 2 x 2 x 5 x 5 x 7 x 17 x 61

Step 4: Therefore, the least common multiple of 1700 and 1708 is 725900.