Least Common Multiple of 1680 and 1687

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 1687 the smallest integer that is 404880 that is divisible by both numbers.

Least Common Multiple (LCM) of 1680 and 1687 is 404880.

LCM(1680,1687) = 404880

LCM of 1680 and 1687

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

LCM of:
and

Least Common Multiple of 1680 and 1687

LCM of 1680 and 1687 is 404880

Least common multiple can be found by multiplying the highest exponent prime factors of 1680 and 1687. First we will calculate the prime factors of 1680 and 1687.

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 1687


7 1687
241 241
1

Prime factors of 1687 are 7,241. Prime factorization of 1687 in exponential form is:

1687 = 71×2411

Now multiplying the highest exponent prime factors to calculate the LCM of 1680 and 1687.

LCM(1680,1687) = 24×31×51×71×2411
LCM(1680,1687) = 404880

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 1687

List of positive integer factors of 1687 that divides 1687 without a remainder.

1, 7, 241, 1687

Least Common Multiple of 1680 and 1687 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 1687, than apply into the LCM equation.

GCF(1680,1687) = 7
LCM(1680,1687) = ( 1680 × 1687) / 7
LCM(1680,1687) = 2834160 / 7
LCM(1680,1687) = 404880

Properties of LCM 1680 and 1687

(i) The LCM of 1687 and 1680 is associative

LCM of 1680 and 1687 = LCM of 1687 and 1680

Related Least Common Multiples of 1680

Related Least Common Multiples of 1687

Frequently Asked Questions on LCM of 1680 and 1687

1. What is the LCM of 1680 and 1687?

Answer: LCM of 1680 and 1687 is 404880.

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 1687?

Answer: Factors of 1687 are 1, 7, 241, 1687. There are 4 integers that are factors of 1687. The greatest factor of 1687 is 1687.

4. How to Find the LCM of 1680 and 1687?

Answer:

Least Common Multiple of 1680 and 1687 = 404880

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 1687

1687 = 7 x 241

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

LCM = 404880 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 241

Step 4: Therefore, the least common multiple of 1680 and 1687 is 404880.