Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1007 and 1010 the smallest integer that is 1017070 that is divisible by both numbers.
Least Common Multiple (LCM) of 1007 and 1010 is 1017070.
LCM(1007,1010) = 1017070
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 1007 and 1010. First we will calculate the prime factors of 1007 and 1010.
Prime Factorization of 1007
19 | 1007 |
53 | 53 |
1 |
Prime factors of 1007 are 19,53. Prime factorization of 1007 in exponential form is:
1007 = 191×531
Prime Factorization of 1010
2 | 1010 |
5 | 505 |
101 | 101 |
1 |
Prime factors of 1010 are 2, 5,101. Prime factorization of 1010 in exponential form is:
1010 = 21×51×1011
Now multiplying the highest exponent prime factors to calculate the LCM of 1007 and 1010.
LCM(1007,1010) = 21×51×191×531×1011
LCM(1007,1010) = 1017070
Factors of 1007
List of positive integer factors of 1007 that divides 1007 without a remainder.
1, 19, 53, 1007
Factors of 1010
List of positive integer factors of 1010 that divides 1010 without a remainder.
1, 2, 5, 10, 101, 202, 505, 1010
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1007 and 1010, than apply into the LCM equation.
GCF(1007,1010) = 1
LCM(1007,1010) = ( 1007 × 1010) / 1
LCM(1007,1010) = 1017070 / 1
LCM(1007,1010) = 1017070
(i) The LCM of 1010 and 1007 is associative
LCM of 1007 and 1010 = LCM of 1010 and 1007
1. What is the LCM of 1007 and 1010?
Answer: LCM of 1007 and 1010 is 1017070.
2. What are the Factors of 1007?
Answer: Factors of 1007 are 1, 19, 53, 1007. There are 4 integers that are factors of 1007. The greatest factor of 1007 is 1007.
3. What are the Factors of 1010?
Answer: Factors of 1010 are 1, 2, 5, 10, 101, 202, 505, 1010. There are 8 integers that are factors of 1010. The greatest factor of 1010 is 1010.
4. How to Find the LCM of 1007 and 1010?
Answer:
Least Common Multiple of 1007 and 1010 = 1017070
Step 1: Find the prime factorization of 1007
1007 = 19 x 53
Step 2: Find the prime factorization of 1010
1010 = 2 x 5 x 101
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1017070 = 2 x 5 x 19 x 53 x 101
Step 4: Therefore, the least common multiple of 1007 and 1010 is 1017070.