Least Common Multiple of 1674 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 1674 and 1680 the smallest integer that is 468720 that is divisible by both numbers.

Least Common Multiple (LCM) of 1674 and 1680 is 468720.

LCM(1674,1680) = 468720

LCM of 1674 and 1680

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

LCM of:
and

Least Common Multiple of 1674 and 1680

LCM of 1674 and 1680 is 468720

Least common multiple can be found by multiplying the highest exponent prime factors of 1674 and 1680. First we will calculate the prime factors of 1674 and 1680.

Prime Factorization of 1674


2 1674
3 837
3 279
3 93
31 31
1

Prime factors of 1674 are 2, 3,31. Prime factorization of 1674 in exponential form is:

1674 = 21×33×311

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 1674 and 1680.

LCM(1674,1680) = 24×33×51×71×311
LCM(1674,1680) = 468720

Factors of 1674

List of positive integer factors of 1674 that divides 1674 without a remainder.

1, 2, 3, 6, 9, 18, 27, 31, 54, 62, 93, 186, 279, 558, 837, 1674

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 1674 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 1674 and 1680, than apply into the LCM equation.

GCF(1674,1680) = 6
LCM(1674,1680) = ( 1674 × 1680) / 6
LCM(1674,1680) = 2812320 / 6
LCM(1674,1680) = 468720

Properties of LCM 1674 and 1680

(i) The LCM of 1680 and 1674 is associative

LCM of 1674 and 1680 = LCM of 1680 and 1674

Related Least Common Multiples of 1674

Related Least Common Multiples of 1680

Frequently Asked Questions on LCM of 1674 and 1680

1. What is the LCM of 1674 and 1680?

Answer: LCM of 1674 and 1680 is 468720.

2. What are the Factors of 1674?

Answer: Factors of 1674 are 1, 2, 3, 6, 9, 18, 27, 31, 54, 62, 93, 186, 279, 558, 837, 1674. There are 16 integers that are factors of 1674. The greatest factor of 1674 is 1674.

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 1674 and 1680?

Answer:

Least Common Multiple of 1674 and 1680 = 468720

Step 1: Find the prime factorization of 1674

1674 = 2 x 3 x 3 x 3 x 31

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 = 468720 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 7 x 31

Step 4: Therefore, the least common multiple of 1674 and 1680 is 468720.