Least Common Multiple of 1680 and 1684

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 1684 the smallest integer that is 707280 that is divisible by both numbers.

Least Common Multiple (LCM) of 1680 and 1684 is 707280.

LCM(1680,1684) = 707280

LCM of 1680 and 1684

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

LCM of:
and

Least Common Multiple of 1680 and 1684

LCM of 1680 and 1684 is 707280

Least common multiple can be found by multiplying the highest exponent prime factors of 1680 and 1684. First we will calculate the prime factors of 1680 and 1684.

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 1684


2 1684
2 842
421 421
1

Prime factors of 1684 are 2,421. Prime factorization of 1684 in exponential form is:

1684 = 22×4211

Now multiplying the highest exponent prime factors to calculate the LCM of 1680 and 1684.

LCM(1680,1684) = 24×31×51×71×4211
LCM(1680,1684) = 707280

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 1684

List of positive integer factors of 1684 that divides 1684 without a remainder.

1, 2, 4, 421, 842, 1684

Least Common Multiple of 1680 and 1684 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 1684, than apply into the LCM equation.

GCF(1680,1684) = 4
LCM(1680,1684) = ( 1680 × 1684) / 4
LCM(1680,1684) = 2829120 / 4
LCM(1680,1684) = 707280

Properties of LCM 1680 and 1684

(i) The LCM of 1684 and 1680 is associative

LCM of 1680 and 1684 = LCM of 1684 and 1680

Related Least Common Multiples of 1680

Related Least Common Multiples of 1684

Frequently Asked Questions on LCM of 1680 and 1684

1. What is the LCM of 1680 and 1684?

Answer: LCM of 1680 and 1684 is 707280.

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 1684?

Answer: Factors of 1684 are 1, 2, 4, 421, 842, 1684. There are 6 integers that are factors of 1684. The greatest factor of 1684 is 1684.

4. How to Find the LCM of 1680 and 1684?

Answer:

Least Common Multiple of 1680 and 1684 = 707280

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 1684

1684 = 2 x 2 x 421

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

LCM = 707280 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 421

Step 4: Therefore, the least common multiple of 1680 and 1684 is 707280.