Least Common Multiple of 1785 and 1792

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1785 and 1792 the smallest integer that is 456960 that is divisible by both numbers.

Least Common Multiple (LCM) of 1785 and 1792 is 456960.

LCM(1785,1792) = 456960

LCM of 1785 and 1792

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

LCM of:
and

Least Common Multiple of 1785 and 1792

LCM of 1785 and 1792 is 456960

Least common multiple can be found by multiplying the highest exponent prime factors of 1785 and 1792. First we will calculate the prime factors of 1785 and 1792.

Prime Factorization of 1785


3 1785
5 595
7 119
17 17
1

Prime factors of 1785 are 3, 5, 7,17. Prime factorization of 1785 in exponential form is:

1785 = 31×51×71×171

Prime Factorization of 1792


2 1792
2 896
2 448
2 224
2 112
2 56
2 28
2 14
7 7
1

Prime factors of 1792 are 2,7. Prime factorization of 1792 in exponential form is:

1792 = 28×71

Now multiplying the highest exponent prime factors to calculate the LCM of 1785 and 1792.

LCM(1785,1792) = 28×31×51×71×171
LCM(1785,1792) = 456960

Factors of 1785

List of positive integer factors of 1785 that divides 1785 without a remainder.

1, 3, 5, 7, 15, 17, 21, 35, 51, 85, 105, 119, 255, 357, 595, 1785

Factors of 1792

List of positive integer factors of 1792 that divides 1792 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 896, 1792

Least Common Multiple of 1785 and 1792 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1785 and 1792, than apply into the LCM equation.

GCF(1785,1792) = 7
LCM(1785,1792) = ( 1785 × 1792) / 7
LCM(1785,1792) = 3198720 / 7
LCM(1785,1792) = 456960

Properties of LCM 1785 and 1792

(i) The LCM of 1792 and 1785 is associative

LCM of 1785 and 1792 = LCM of 1792 and 1785

Related Least Common Multiples of 1785

Related Least Common Multiples of 1792

Frequently Asked Questions on LCM of 1785 and 1792

1. What is the LCM of 1785 and 1792?

Answer: LCM of 1785 and 1792 is 456960.

2. What are the Factors of 1785?

Answer: Factors of 1785 are 1, 3, 5, 7, 15, 17, 21, 35, 51, 85, 105, 119, 255, 357, 595, 1785. There are 16 integers that are factors of 1785. The greatest factor of 1785 is 1785.

3. What are the Factors of 1792?

Answer: Factors of 1792 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 896, 1792. There are 18 integers that are factors of 1792. The greatest factor of 1792 is 1792.

4. How to Find the LCM of 1785 and 1792?

Answer:

Least Common Multiple of 1785 and 1792 = 456960

Step 1: Find the prime factorization of 1785

1785 = 3 x 5 x 7 x 17

Step 2: Find the prime factorization of 1792

1792 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 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 = 456960 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 1785 and 1792 is 456960.