Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8010 and 8014 the smallest integer that is 32096070 that is divisible by both numbers.
Least Common Multiple (LCM) of 8010 and 8014 is 32096070.
LCM(8010,8014) = 32096070
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 8010 and 8014. First we will calculate the prime factors of 8010 and 8014.
Prime Factorization of 8010
2 | 8010 |
3 | 4005 |
3 | 1335 |
5 | 445 |
89 | 89 |
1 |
Prime factors of 8010 are 2, 3, 5,89. Prime factorization of 8010 in exponential form is:
8010 = 21×32×51×891
Prime Factorization of 8014
2 | 8014 |
4007 | 4007 |
1 |
Prime factors of 8014 are 2,4007. Prime factorization of 8014 in exponential form is:
8014 = 21×40071
Now multiplying the highest exponent prime factors to calculate the LCM of 8010 and 8014.
LCM(8010,8014) = 21×32×51×891×40071
LCM(8010,8014) = 32096070
Factors of 8010
List of positive integer factors of 8010 that divides 8010 without a remainder.
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 89, 90, 178, 267, 445, 534, 801, 890, 1335, 1602, 2670, 4005, 8010
Factors of 8014
List of positive integer factors of 8014 that divides 8014 without a remainder.
1, 2, 4007, 8014
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8010 and 8014, than apply into the LCM equation.
GCF(8010,8014) = 2
LCM(8010,8014) = ( 8010 × 8014) / 2
LCM(8010,8014) = 64192140 / 2
LCM(8010,8014) = 32096070
(i) The LCM of 8014 and 8010 is associative
LCM of 8010 and 8014 = LCM of 8014 and 8010
1. What is the LCM of 8010 and 8014?
Answer: LCM of 8010 and 8014 is 32096070.
2. What are the Factors of 8010?
Answer: Factors of 8010 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 89, 90, 178, 267, 445, 534, 801, 890, 1335, 1602, 2670, 4005, 8010. There are 24 integers that are factors of 8010. The greatest factor of 8010 is 8010.
3. What are the Factors of 8014?
Answer: Factors of 8014 are 1, 2, 4007, 8014. There are 4 integers that are factors of 8014. The greatest factor of 8014 is 8014.
4. How to Find the LCM of 8010 and 8014?
Answer:
Least Common Multiple of 8010 and 8014 = 32096070
Step 1: Find the prime factorization of 8010
8010 = 2 x 3 x 3 x 5 x 89
Step 2: Find the prime factorization of 8014
8014 = 2 x 4007
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 32096070 = 2 x 3 x 3 x 5 x 89 x 4007
Step 4: Therefore, the least common multiple of 8010 and 8014 is 32096070.