Least Common Multiple of 1680 and 1686

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 1686 the smallest integer that is 472080 that is divisible by both numbers.

Least Common Multiple (LCM) of 1680 and 1686 is 472080.

LCM(1680,1686) = 472080

LCM of 1680 and 1686

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

LCM of:
and

Least Common Multiple of 1680 and 1686

LCM of 1680 and 1686 is 472080

Least common multiple can be found by multiplying the highest exponent prime factors of 1680 and 1686. First we will calculate the prime factors of 1680 and 1686.

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 1686


2 1686
3 843
281 281
1

Prime factors of 1686 are 2, 3,281. Prime factorization of 1686 in exponential form is:

1686 = 21×31×2811

Now multiplying the highest exponent prime factors to calculate the LCM of 1680 and 1686.

LCM(1680,1686) = 24×31×51×71×2811
LCM(1680,1686) = 472080

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 1686

List of positive integer factors of 1686 that divides 1686 without a remainder.

1, 2, 3, 6, 281, 562, 843, 1686

Least Common Multiple of 1680 and 1686 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 1686, than apply into the LCM equation.

GCF(1680,1686) = 6
LCM(1680,1686) = ( 1680 × 1686) / 6
LCM(1680,1686) = 2832480 / 6
LCM(1680,1686) = 472080

Properties of LCM 1680 and 1686

(i) The LCM of 1686 and 1680 is associative

LCM of 1680 and 1686 = LCM of 1686 and 1680

Related Least Common Multiples of 1680

Related Least Common Multiples of 1686

Frequently Asked Questions on LCM of 1680 and 1686

1. What is the LCM of 1680 and 1686?

Answer: LCM of 1680 and 1686 is 472080.

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 1686?

Answer: Factors of 1686 are 1, 2, 3, 6, 281, 562, 843, 1686. There are 8 integers that are factors of 1686. The greatest factor of 1686 is 1686.

4. How to Find the LCM of 1680 and 1686?

Answer:

Least Common Multiple of 1680 and 1686 = 472080

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 1686

1686 = 2 x 3 x 281

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

LCM = 472080 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 281

Step 4: Therefore, the least common multiple of 1680 and 1686 is 472080.