Least Common Multiple of 1029 and 1035

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 1035 the smallest integer that is 355005 that is divisible by both numbers.

Least Common Multiple (LCM) of 1029 and 1035 is 355005.

LCM(1029,1035) = 355005

LCM of 1029 and 1035

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

LCM of:
and

Least Common Multiple of 1029 and 1035

LCM of 1029 and 1035 is 355005

Least common multiple can be found by multiplying the highest exponent prime factors of 1029 and 1035. First we will calculate the prime factors of 1029 and 1035.

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 1035


3 1035
3 345
5 115
23 23
1

Prime factors of 1035 are 3, 5,23. Prime factorization of 1035 in exponential form is:

1035 = 32×51×231

Now multiplying the highest exponent prime factors to calculate the LCM of 1029 and 1035.

LCM(1029,1035) = 32×51×73×231
LCM(1029,1035) = 355005

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 1035

List of positive integer factors of 1035 that divides 1035 without a remainder.

1, 3, 5, 9, 15, 23, 45, 69, 115, 207, 345, 1035

Least Common Multiple of 1029 and 1035 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 1035, than apply into the LCM equation.

GCF(1029,1035) = 3
LCM(1029,1035) = ( 1029 × 1035) / 3
LCM(1029,1035) = 1065015 / 3
LCM(1029,1035) = 355005

Properties of LCM 1029 and 1035

(i) The LCM of 1035 and 1029 is associative

LCM of 1029 and 1035 = LCM of 1035 and 1029

Related Least Common Multiples of 1029

Related Least Common Multiples of 1035

Frequently Asked Questions on LCM of 1029 and 1035

1. What is the LCM of 1029 and 1035?

Answer: LCM of 1029 and 1035 is 355005.

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 1035?

Answer: Factors of 1035 are 1, 3, 5, 9, 15, 23, 45, 69, 115, 207, 345, 1035. There are 12 integers that are factors of 1035. The greatest factor of 1035 is 1035.

4. How to Find the LCM of 1029 and 1035?

Answer:

Least Common Multiple of 1029 and 1035 = 355005

Step 1: Find the prime factorization of 1029

1029 = 3 x 7 x 7 x 7

Step 2: Find the prime factorization of 1035

1035 = 3 x 3 x 5 x 23

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

LCM = 355005 = 3 x 3 x 5 x 7 x 7 x 7 x 23

Step 4: Therefore, the least common multiple of 1029 and 1035 is 355005.