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 2033 the smallest integer that is 4131056 that is divisible by both numbers.
Least Common Multiple (LCM) of 2032 and 2033 is 4131056.
LCM(2032,2033) = 4131056
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 2033. First we will calculate the prime factors of 2032 and 2033.
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 2033
19 | 2033 |
107 | 107 |
1 |
Prime factors of 2033 are 19,107. Prime factorization of 2033 in exponential form is:
2033 = 191×1071
Now multiplying the highest exponent prime factors to calculate the LCM of 2032 and 2033.
LCM(2032,2033) = 24×191×1071×1271
LCM(2032,2033) = 4131056
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 2033
List of positive integer factors of 2033 that divides 2033 without a remainder.
1, 19, 107, 2033
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2032 and 2033, than apply into the LCM equation.
GCF(2032,2033) = 1
LCM(2032,2033) = ( 2032 × 2033) / 1
LCM(2032,2033) = 4131056 / 1
LCM(2032,2033) = 4131056
(i) The LCM of 2033 and 2032 is associative
LCM of 2032 and 2033 = LCM of 2033 and 2032
1. What is the LCM of 2032 and 2033?
Answer: LCM of 2032 and 2033 is 4131056.
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 2033?
Answer: Factors of 2033 are 1, 19, 107, 2033. There are 4 integers that are factors of 2033. The greatest factor of 2033 is 2033.
4. How to Find the LCM of 2032 and 2033?
Answer:
Least Common Multiple of 2032 and 2033 = 4131056
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 2033
2033 = 19 x 107
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4131056 = 2 x 2 x 2 x 2 x 19 x 107 x 127
Step 4: Therefore, the least common multiple of 2032 and 2033 is 4131056.