Least Common Multiple of 1680 and 1685

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1680 and 1685 the smallest integer that is 566160 that is divisible by both numbers.

Least Common Multiple (LCM) of 1680 and 1685 is 566160.

LCM(1680,1685) = 566160

LCM of 1680 and 1685

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

LCM of:
and

Least Common Multiple of 1680 and 1685

LCM of 1680 and 1685 is 566160

Least common multiple can be found by multiplying the highest exponent prime factors of 1680 and 1685. First we will calculate the prime factors of 1680 and 1685.

Prime Factorization of 1680


2 1680
2 840
2 420
2 210
3 105
5 35
7 7
1

Prime factors of 1680 are 2, 3, 5,7. Prime factorization of 1680 in exponential form is:

1680 = 24×31×51×71

Prime Factorization of 1685


5 1685
337 337
1

Prime factors of 1685 are 5,337. Prime factorization of 1685 in exponential form is:

1685 = 51×3371

Now multiplying the highest exponent prime factors to calculate the LCM of 1680 and 1685.

LCM(1680,1685) = 24×31×51×71×3371
LCM(1680,1685) = 566160

Factors of 1680

List of positive integer factors of 1680 that divides 1680 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680

Factors of 1685

List of positive integer factors of 1685 that divides 1685 without a remainder.

1, 5, 337, 1685

Least Common Multiple of 1680 and 1685 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1680 and 1685, than apply into the LCM equation.

GCF(1680,1685) = 5
LCM(1680,1685) = ( 1680 × 1685) / 5
LCM(1680,1685) = 2830800 / 5
LCM(1680,1685) = 566160

Properties of LCM 1680 and 1685

(i) The LCM of 1685 and 1680 is associative

LCM of 1680 and 1685 = LCM of 1685 and 1680

Related Least Common Multiples of 1680

Related Least Common Multiples of 1685

Frequently Asked Questions on LCM of 1680 and 1685

1. What is the LCM of 1680 and 1685?

Answer: LCM of 1680 and 1685 is 566160.

2. What are the Factors of 1680?

Answer: Factors of 1680 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680. There are 40 integers that are factors of 1680. The greatest factor of 1680 is 1680.

3. What are the Factors of 1685?

Answer: Factors of 1685 are 1, 5, 337, 1685. There are 4 integers that are factors of 1685. The greatest factor of 1685 is 1685.

4. How to Find the LCM of 1680 and 1685?

Answer:

Least Common Multiple of 1680 and 1685 = 566160

Step 1: Find the prime factorization of 1680

1680 = 2 x 2 x 2 x 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 1685

1685 = 5 x 337

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

LCM = 566160 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 337

Step 4: Therefore, the least common multiple of 1680 and 1685 is 566160.