Least Common Multiple of 1689 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 1689 and 1696 the smallest integer that is 2864544 that is divisible by both numbers.

Least Common Multiple (LCM) of 1689 and 1696 is 2864544.

LCM(1689,1696) = 2864544

LCM of 1689 and 1696

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

LCM of:
and

Least Common Multiple of 1689 and 1696

LCM of 1689 and 1696 is 2864544

Least common multiple can be found by multiplying the highest exponent prime factors of 1689 and 1696. First we will calculate the prime factors of 1689 and 1696.

Prime Factorization of 1689


3 1689
563 563
1

Prime factors of 1689 are 3,563. Prime factorization of 1689 in exponential form is:

1689 = 31×5631

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 1689 and 1696.

LCM(1689,1696) = 25×31×531×5631
LCM(1689,1696) = 2864544

Factors of 1689

List of positive integer factors of 1689 that divides 1689 without a remainder.

1, 3, 563, 1689

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 1689 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 1689 and 1696, than apply into the LCM equation.

GCF(1689,1696) = 1
LCM(1689,1696) = ( 1689 × 1696) / 1
LCM(1689,1696) = 2864544 / 1
LCM(1689,1696) = 2864544

Properties of LCM 1689 and 1696

(i) The LCM of 1696 and 1689 is associative

LCM of 1689 and 1696 = LCM of 1696 and 1689

Related Least Common Multiples of 1689

Related Least Common Multiples of 1696

Frequently Asked Questions on LCM of 1689 and 1696

1. What is the LCM of 1689 and 1696?

Answer: LCM of 1689 and 1696 is 2864544.

2. What are the Factors of 1689?

Answer: Factors of 1689 are 1, 3, 563, 1689. There are 4 integers that are factors of 1689. The greatest factor of 1689 is 1689.

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 1689 and 1696?

Answer:

Least Common Multiple of 1689 and 1696 = 2864544

Step 1: Find the prime factorization of 1689

1689 = 3 x 563

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 = 2864544 = 2 x 2 x 2 x 2 x 2 x 3 x 53 x 563

Step 4: Therefore, the least common multiple of 1689 and 1696 is 2864544.