Least Common Multiple of 1742 and 1749

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1742 and 1749 the smallest integer that is 3046758 that is divisible by both numbers.

Least Common Multiple (LCM) of 1742 and 1749 is 3046758.

LCM(1742,1749) = 3046758

LCM of 1742 and 1749

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

LCM of:
and

Least Common Multiple of 1742 and 1749

LCM of 1742 and 1749 is 3046758

Least common multiple can be found by multiplying the highest exponent prime factors of 1742 and 1749. First we will calculate the prime factors of 1742 and 1749.

Prime Factorization of 1742


2 1742
13 871
67 67
1

Prime factors of 1742 are 2, 13,67. Prime factorization of 1742 in exponential form is:

1742 = 21×131×671

Prime Factorization of 1749


3 1749
11 583
53 53
1

Prime factors of 1749 are 3, 11,53. Prime factorization of 1749 in exponential form is:

1749 = 31×111×531

Now multiplying the highest exponent prime factors to calculate the LCM of 1742 and 1749.

LCM(1742,1749) = 21×31×111×131×531×671
LCM(1742,1749) = 3046758

Factors of 1742

List of positive integer factors of 1742 that divides 1742 without a remainder.

1, 2, 13, 26, 67, 134, 871, 1742

Factors of 1749

List of positive integer factors of 1749 that divides 1749 without a remainder.

1, 3, 11, 33, 53, 159, 583, 1749

Least Common Multiple of 1742 and 1749 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1742 and 1749, than apply into the LCM equation.

GCF(1742,1749) = 1
LCM(1742,1749) = ( 1742 × 1749) / 1
LCM(1742,1749) = 3046758 / 1
LCM(1742,1749) = 3046758

Properties of LCM 1742 and 1749

(i) The LCM of 1749 and 1742 is associative

LCM of 1742 and 1749 = LCM of 1749 and 1742

Related Least Common Multiples of 1742

Related Least Common Multiples of 1749

Frequently Asked Questions on LCM of 1742 and 1749

1. What is the LCM of 1742 and 1749?

Answer: LCM of 1742 and 1749 is 3046758.

2. What are the Factors of 1742?

Answer: Factors of 1742 are 1, 2, 13, 26, 67, 134, 871, 1742. There are 8 integers that are factors of 1742. The greatest factor of 1742 is 1742.

3. What are the Factors of 1749?

Answer: Factors of 1749 are 1, 3, 11, 33, 53, 159, 583, 1749. There are 8 integers that are factors of 1749. The greatest factor of 1749 is 1749.

4. How to Find the LCM of 1742 and 1749?

Answer:

Least Common Multiple of 1742 and 1749 = 3046758

Step 1: Find the prime factorization of 1742

1742 = 2 x 13 x 67

Step 2: Find the prime factorization of 1749

1749 = 3 x 11 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 = 3046758 = 2 x 3 x 11 x 13 x 53 x 67

Step 4: Therefore, the least common multiple of 1742 and 1749 is 3046758.