Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1009 and 1010 the smallest integer that is 1019090 that is divisible by both numbers.
Least Common Multiple (LCM) of 1009 and 1010 is 1019090.
LCM(1009,1010) = 1019090
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 1009 and 1010. First we will calculate the prime factors of 1009 and 1010.
Prime Factorization of 1009
1009 | 1009 |
1 |
Prime factors of 1009 are 1009. Prime factorization of 1009 in exponential form is:
1009 = 10091
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 1009 and 1010.
LCM(1009,1010) = 21×51×1011×10091
LCM(1009,1010) = 1019090
Factors of 1009
List of positive integer factors of 1009 that divides 1009 without a remainder.
1, 1009
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 1009 and 1010, than apply into the LCM equation.
GCF(1009,1010) = 1
LCM(1009,1010) = ( 1009 × 1010) / 1
LCM(1009,1010) = 1019090 / 1
LCM(1009,1010) = 1019090
(i) The LCM of 1010 and 1009 is associative
LCM of 1009 and 1010 = LCM of 1010 and 1009
1. What is the LCM of 1009 and 1010?
Answer: LCM of 1009 and 1010 is 1019090.
2. What are the Factors of 1009?
Answer: Factors of 1009 are 1, 1009. There are 2 integers that are factors of 1009. The greatest factor of 1009 is 1009.
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 1009 and 1010?
Answer:
Least Common Multiple of 1009 and 1010 = 1019090
Step 1: Find the prime factorization of 1009
1009 = 1009
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 = 1019090 = 2 x 5 x 101 x 1009
Step 4: Therefore, the least common multiple of 1009 and 1010 is 1019090.