Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2996 and 3003 the smallest integer that is 1285284 that is divisible by both numbers.
Least Common Multiple (LCM) of 2996 and 3003 is 1285284.
LCM(2996,3003) = 1285284
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 2996 and 3003. First we will calculate the prime factors of 2996 and 3003.
Prime Factorization of 2996
2 | 2996 |
2 | 1498 |
7 | 749 |
107 | 107 |
1 |
Prime factors of 2996 are 2, 7,107. Prime factorization of 2996 in exponential form is:
2996 = 22×71×1071
Prime Factorization of 3003
3 | 3003 |
7 | 1001 |
11 | 143 |
13 | 13 |
1 |
Prime factors of 3003 are 3, 7, 11,13. Prime factorization of 3003 in exponential form is:
3003 = 31×71×111×131
Now multiplying the highest exponent prime factors to calculate the LCM of 2996 and 3003.
LCM(2996,3003) = 22×31×71×111×131×1071
LCM(2996,3003) = 1285284
Factors of 2996
List of positive integer factors of 2996 that divides 2996 without a remainder.
1, 2, 4, 7, 14, 28, 107, 214, 428, 749, 1498, 2996
Factors of 3003
List of positive integer factors of 3003 that divides 3003 without a remainder.
1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 143, 231, 273, 429, 1001, 3003
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2996 and 3003, than apply into the LCM equation.
GCF(2996,3003) = 7
LCM(2996,3003) = ( 2996 × 3003) / 7
LCM(2996,3003) = 8996988 / 7
LCM(2996,3003) = 1285284
(i) The LCM of 3003 and 2996 is associative
LCM of 2996 and 3003 = LCM of 3003 and 2996
1. What is the LCM of 2996 and 3003?
Answer: LCM of 2996 and 3003 is 1285284.
2. What are the Factors of 2996?
Answer: Factors of 2996 are 1, 2, 4, 7, 14, 28, 107, 214, 428, 749, 1498, 2996. There are 12 integers that are factors of 2996. The greatest factor of 2996 is 2996.
3. What are the Factors of 3003?
Answer: Factors of 3003 are 1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 143, 231, 273, 429, 1001, 3003. There are 16 integers that are factors of 3003. The greatest factor of 3003 is 3003.
4. How to Find the LCM of 2996 and 3003?
Answer:
Least Common Multiple of 2996 and 3003 = 1285284
Step 1: Find the prime factorization of 2996
2996 = 2 x 2 x 7 x 107
Step 2: Find the prime factorization of 3003
3003 = 3 x 7 x 11 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1285284 = 2 x 2 x 3 x 7 x 11 x 13 x 107
Step 4: Therefore, the least common multiple of 2996 and 3003 is 1285284.