Least Common Multiple of 1680 and 1688

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 1688 the smallest integer that is 354480 that is divisible by both numbers.

Least Common Multiple (LCM) of 1680 and 1688 is 354480.

LCM(1680,1688) = 354480

LCM of 1680 and 1688

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

LCM of:
and

Least Common Multiple of 1680 and 1688

LCM of 1680 and 1688 is 354480

Least common multiple can be found by multiplying the highest exponent prime factors of 1680 and 1688. First we will calculate the prime factors of 1680 and 1688.

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 1688


2 1688
2 844
2 422
211 211
1

Prime factors of 1688 are 2,211. Prime factorization of 1688 in exponential form is:

1688 = 23×2111

Now multiplying the highest exponent prime factors to calculate the LCM of 1680 and 1688.

LCM(1680,1688) = 24×31×51×71×2111
LCM(1680,1688) = 354480

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 1688

List of positive integer factors of 1688 that divides 1688 without a remainder.

1, 2, 4, 8, 211, 422, 844, 1688

Least Common Multiple of 1680 and 1688 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 1688, than apply into the LCM equation.

GCF(1680,1688) = 8
LCM(1680,1688) = ( 1680 × 1688) / 8
LCM(1680,1688) = 2835840 / 8
LCM(1680,1688) = 354480

Properties of LCM 1680 and 1688

(i) The LCM of 1688 and 1680 is associative

LCM of 1680 and 1688 = LCM of 1688 and 1680

Related Least Common Multiples of 1680

Related Least Common Multiples of 1688

Frequently Asked Questions on LCM of 1680 and 1688

1. What is the LCM of 1680 and 1688?

Answer: LCM of 1680 and 1688 is 354480.

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 1688?

Answer: Factors of 1688 are 1, 2, 4, 8, 211, 422, 844, 1688. There are 8 integers that are factors of 1688. The greatest factor of 1688 is 1688.

4. How to Find the LCM of 1680 and 1688?

Answer:

Least Common Multiple of 1680 and 1688 = 354480

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 1688

1688 = 2 x 2 x 2 x 211

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

LCM = 354480 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 211

Step 4: Therefore, the least common multiple of 1680 and 1688 is 354480.