Least Common Multiple of 1029 and 1032

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1029 and 1032 the smallest integer that is 353976 that is divisible by both numbers.

Least Common Multiple (LCM) of 1029 and 1032 is 353976.

LCM(1029,1032) = 353976

LCM of 1029 and 1032

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

LCM of:
and

Least Common Multiple of 1029 and 1032

LCM of 1029 and 1032 is 353976

Least common multiple can be found by multiplying the highest exponent prime factors of 1029 and 1032. First we will calculate the prime factors of 1029 and 1032.

Prime Factorization of 1029


3 1029
7 343
7 49
7 7
1

Prime factors of 1029 are 3,7. Prime factorization of 1029 in exponential form is:

1029 = 31×73

Prime Factorization of 1032


2 1032
2 516
2 258
3 129
43 43
1

Prime factors of 1032 are 2, 3,43. Prime factorization of 1032 in exponential form is:

1032 = 23×31×431

Now multiplying the highest exponent prime factors to calculate the LCM of 1029 and 1032.

LCM(1029,1032) = 23×31×73×431
LCM(1029,1032) = 353976

Factors of 1029

List of positive integer factors of 1029 that divides 1029 without a remainder.

1, 3, 7, 21, 49, 147, 343, 1029

Factors of 1032

List of positive integer factors of 1032 that divides 1032 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 43, 86, 129, 172, 258, 344, 516, 1032

Least Common Multiple of 1029 and 1032 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1029 and 1032, than apply into the LCM equation.

GCF(1029,1032) = 3
LCM(1029,1032) = ( 1029 × 1032) / 3
LCM(1029,1032) = 1061928 / 3
LCM(1029,1032) = 353976

Properties of LCM 1029 and 1032

(i) The LCM of 1032 and 1029 is associative

LCM of 1029 and 1032 = LCM of 1032 and 1029

Related Least Common Multiples of 1029

Related Least Common Multiples of 1032

Frequently Asked Questions on LCM of 1029 and 1032

1. What is the LCM of 1029 and 1032?

Answer: LCM of 1029 and 1032 is 353976.

2. What are the Factors of 1029?

Answer: Factors of 1029 are 1, 3, 7, 21, 49, 147, 343, 1029. There are 8 integers that are factors of 1029. The greatest factor of 1029 is 1029.

3. What are the Factors of 1032?

Answer: Factors of 1032 are 1, 2, 3, 4, 6, 8, 12, 24, 43, 86, 129, 172, 258, 344, 516, 1032. There are 16 integers that are factors of 1032. The greatest factor of 1032 is 1032.

4. How to Find the LCM of 1029 and 1032?

Answer:

Least Common Multiple of 1029 and 1032 = 353976

Step 1: Find the prime factorization of 1029

1029 = 3 x 7 x 7 x 7

Step 2: Find the prime factorization of 1032

1032 = 2 x 2 x 2 x 3 x 43

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

LCM = 353976 = 2 x 2 x 2 x 3 x 7 x 7 x 7 x 43

Step 4: Therefore, the least common multiple of 1029 and 1032 is 353976.