Least Common Multiple of 1688 and 1696

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1688 and 1696 the smallest integer that is 357856 that is divisible by both numbers.

Least Common Multiple (LCM) of 1688 and 1696 is 357856.

LCM(1688,1696) = 357856

LCM of 1688 and 1696

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

LCM of:
and

Least Common Multiple of 1688 and 1696

LCM of 1688 and 1696 is 357856

Least common multiple can be found by multiplying the highest exponent prime factors of 1688 and 1696. First we will calculate the prime factors of 1688 and 1696.

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

Prime Factorization of 1696


2 1696
2 848
2 424
2 212
2 106
53 53
1

Prime factors of 1696 are 2,53. Prime factorization of 1696 in exponential form is:

1696 = 25×531

Now multiplying the highest exponent prime factors to calculate the LCM of 1688 and 1696.

LCM(1688,1696) = 25×531×2111
LCM(1688,1696) = 357856

Factors of 1688

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

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

Factors of 1696

List of positive integer factors of 1696 that divides 1696 without a remainder.

1, 2, 4, 8, 16, 32, 53, 106, 212, 424, 848, 1696

Least Common Multiple of 1688 and 1696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1688 and 1696, than apply into the LCM equation.

GCF(1688,1696) = 8
LCM(1688,1696) = ( 1688 × 1696) / 8
LCM(1688,1696) = 2862848 / 8
LCM(1688,1696) = 357856

Properties of LCM 1688 and 1696

(i) The LCM of 1696 and 1688 is associative

LCM of 1688 and 1696 = LCM of 1696 and 1688

Related Least Common Multiples of 1688

Related Least Common Multiples of 1696

Frequently Asked Questions on LCM of 1688 and 1696

1. What is the LCM of 1688 and 1696?

Answer: LCM of 1688 and 1696 is 357856.

2. 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.

3. What are the Factors of 1696?

Answer: Factors of 1696 are 1, 2, 4, 8, 16, 32, 53, 106, 212, 424, 848, 1696. There are 12 integers that are factors of 1696. The greatest factor of 1696 is 1696.

4. How to Find the LCM of 1688 and 1696?

Answer:

Least Common Multiple of 1688 and 1696 = 357856

Step 1: Find the prime factorization of 1688

1688 = 2 x 2 x 2 x 211

Step 2: Find the prime factorization of 1696

1696 = 2 x 2 x 2 x 2 x 2 x 53

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

LCM = 357856 = 2 x 2 x 2 x 2 x 2 x 53 x 211

Step 4: Therefore, the least common multiple of 1688 and 1696 is 357856.