Least Common Multiple of 1675 and 1680

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1675 and 1680 the smallest integer that is 562800 that is divisible by both numbers.

Least Common Multiple (LCM) of 1675 and 1680 is 562800.

LCM(1675,1680) = 562800

LCM of 1675 and 1680

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

LCM of:
and

Least Common Multiple of 1675 and 1680

LCM of 1675 and 1680 is 562800

Least common multiple can be found by multiplying the highest exponent prime factors of 1675 and 1680. First we will calculate the prime factors of 1675 and 1680.

Prime Factorization of 1675


5 1675
5 335
67 67
1

Prime factors of 1675 are 5,67. Prime factorization of 1675 in exponential form is:

1675 = 52×671

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1675 and 1680.

LCM(1675,1680) = 24×31×52×71×671
LCM(1675,1680) = 562800

Factors of 1675

List of positive integer factors of 1675 that divides 1675 without a remainder.

1, 5, 25, 67, 335, 1675

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

Least Common Multiple of 1675 and 1680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1675 and 1680, than apply into the LCM equation.

GCF(1675,1680) = 5
LCM(1675,1680) = ( 1675 × 1680) / 5
LCM(1675,1680) = 2814000 / 5
LCM(1675,1680) = 562800

Properties of LCM 1675 and 1680

(i) The LCM of 1680 and 1675 is associative

LCM of 1675 and 1680 = LCM of 1680 and 1675

Related Least Common Multiples of 1675

Related Least Common Multiples of 1680

Frequently Asked Questions on LCM of 1675 and 1680

1. What is the LCM of 1675 and 1680?

Answer: LCM of 1675 and 1680 is 562800.

2. What are the Factors of 1675?

Answer: Factors of 1675 are 1, 5, 25, 67, 335, 1675. There are 6 integers that are factors of 1675. The greatest factor of 1675 is 1675.

3. 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.

4. How to Find the LCM of 1675 and 1680?

Answer:

Least Common Multiple of 1675 and 1680 = 562800

Step 1: Find the prime factorization of 1675

1675 = 5 x 5 x 67

Step 2: Find the prime factorization of 1680

1680 = 2 x 2 x 2 x 2 x 3 x 5 x 7

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

LCM = 562800 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 67

Step 4: Therefore, the least common multiple of 1675 and 1680 is 562800.