Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7240 and 7242 the smallest integer that is 26216040 that is divisible by both numbers.
Least Common Multiple (LCM) of 7240 and 7242 is 26216040.
LCM(7240,7242) = 26216040
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 7240 and 7242. First we will calculate the prime factors of 7240 and 7242.
Prime Factorization of 7240
2 | 7240 |
2 | 3620 |
2 | 1810 |
5 | 905 |
181 | 181 |
1 |
Prime factors of 7240 are 2, 5,181. Prime factorization of 7240 in exponential form is:
7240 = 23×51×1811
Prime Factorization of 7242
2 | 7242 |
3 | 3621 |
17 | 1207 |
71 | 71 |
1 |
Prime factors of 7242 are 2, 3, 17,71. Prime factorization of 7242 in exponential form is:
7242 = 21×31×171×711
Now multiplying the highest exponent prime factors to calculate the LCM of 7240 and 7242.
LCM(7240,7242) = 23×31×51×171×711×1811
LCM(7240,7242) = 26216040
Factors of 7240
List of positive integer factors of 7240 that divides 7240 without a remainder.
1, 2, 4, 5, 8, 10, 20, 40, 181, 362, 724, 905, 1448, 1810, 3620, 7240
Factors of 7242
List of positive integer factors of 7242 that divides 7242 without a remainder.
1, 2, 3, 6, 17, 34, 51, 71, 102, 142, 213, 426, 1207, 2414, 3621, 7242
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7240 and 7242, than apply into the LCM equation.
GCF(7240,7242) = 2
LCM(7240,7242) = ( 7240 × 7242) / 2
LCM(7240,7242) = 52432080 / 2
LCM(7240,7242) = 26216040
(i) The LCM of 7242 and 7240 is associative
LCM of 7240 and 7242 = LCM of 7242 and 7240
1. What is the LCM of 7240 and 7242?
Answer: LCM of 7240 and 7242 is 26216040.
2. What are the Factors of 7240?
Answer: Factors of 7240 are 1, 2, 4, 5, 8, 10, 20, 40, 181, 362, 724, 905, 1448, 1810, 3620, 7240. There are 16 integers that are factors of 7240. The greatest factor of 7240 is 7240.
3. What are the Factors of 7242?
Answer: Factors of 7242 are 1, 2, 3, 6, 17, 34, 51, 71, 102, 142, 213, 426, 1207, 2414, 3621, 7242. There are 16 integers that are factors of 7242. The greatest factor of 7242 is 7242.
4. How to Find the LCM of 7240 and 7242?
Answer:
Least Common Multiple of 7240 and 7242 = 26216040
Step 1: Find the prime factorization of 7240
7240 = 2 x 2 x 2 x 5 x 181
Step 2: Find the prime factorization of 7242
7242 = 2 x 3 x 17 x 71
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 26216040 = 2 x 2 x 2 x 3 x 5 x 17 x 71 x 181
Step 4: Therefore, the least common multiple of 7240 and 7242 is 26216040.