Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2032 and 2035 the smallest integer that is 4135120 that is divisible by both numbers.
Least Common Multiple (LCM) of 2032 and 2035 is 4135120.
LCM(2032,2035) = 4135120
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 2032 and 2035. First we will calculate the prime factors of 2032 and 2035.
Prime Factorization of 2032
2 | 2032 |
2 | 1016 |
2 | 508 |
2 | 254 |
127 | 127 |
1 |
Prime factors of 2032 are 2,127. Prime factorization of 2032 in exponential form is:
2032 = 24×1271
Prime Factorization of 2035
5 | 2035 |
11 | 407 |
37 | 37 |
1 |
Prime factors of 2035 are 5, 11,37. Prime factorization of 2035 in exponential form is:
2035 = 51×111×371
Now multiplying the highest exponent prime factors to calculate the LCM of 2032 and 2035.
LCM(2032,2035) = 24×51×111×371×1271
LCM(2032,2035) = 4135120
Factors of 2032
List of positive integer factors of 2032 that divides 2032 without a remainder.
1, 2, 4, 8, 16, 127, 254, 508, 1016, 2032
Factors of 2035
List of positive integer factors of 2035 that divides 2035 without a remainder.
1, 5, 11, 37, 55, 185, 407, 2035
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2032 and 2035, than apply into the LCM equation.
GCF(2032,2035) = 1
LCM(2032,2035) = ( 2032 × 2035) / 1
LCM(2032,2035) = 4135120 / 1
LCM(2032,2035) = 4135120
(i) The LCM of 2035 and 2032 is associative
LCM of 2032 and 2035 = LCM of 2035 and 2032
1. What is the LCM of 2032 and 2035?
Answer: LCM of 2032 and 2035 is 4135120.
2. What are the Factors of 2032?
Answer: Factors of 2032 are 1, 2, 4, 8, 16, 127, 254, 508, 1016, 2032. There are 10 integers that are factors of 2032. The greatest factor of 2032 is 2032.
3. What are the Factors of 2035?
Answer: Factors of 2035 are 1, 5, 11, 37, 55, 185, 407, 2035. There are 8 integers that are factors of 2035. The greatest factor of 2035 is 2035.
4. How to Find the LCM of 2032 and 2035?
Answer:
Least Common Multiple of 2032 and 2035 = 4135120
Step 1: Find the prime factorization of 2032
2032 = 2 x 2 x 2 x 2 x 127
Step 2: Find the prime factorization of 2035
2035 = 5 x 11 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4135120 = 2 x 2 x 2 x 2 x 5 x 11 x 37 x 127
Step 4: Therefore, the least common multiple of 2032 and 2035 is 4135120.