Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7272 and 7280 the smallest integer that is 6617520 that is divisible by both numbers.
Least Common Multiple (LCM) of 7272 and 7280 is 6617520.
LCM(7272,7280) = 6617520
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 7272 and 7280. First we will calculate the prime factors of 7272 and 7280.
Prime Factorization of 7272
2 | 7272 |
2 | 3636 |
2 | 1818 |
3 | 909 |
3 | 303 |
101 | 101 |
1 |
Prime factors of 7272 are 2, 3,101. Prime factorization of 7272 in exponential form is:
7272 = 23×32×1011
Prime Factorization of 7280
2 | 7280 |
2 | 3640 |
2 | 1820 |
2 | 910 |
5 | 455 |
7 | 91 |
13 | 13 |
1 |
Prime factors of 7280 are 2, 5, 7,13. Prime factorization of 7280 in exponential form is:
7280 = 24×51×71×131
Now multiplying the highest exponent prime factors to calculate the LCM of 7272 and 7280.
LCM(7272,7280) = 24×32×51×71×131×1011
LCM(7272,7280) = 6617520
Factors of 7272
List of positive integer factors of 7272 that divides 7272 without a remainder.
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 101, 202, 303, 404, 606, 808, 909, 1212, 1818, 2424, 3636, 7272
Factors of 7280
List of positive integer factors of 7280 that divides 7280 without a remainder.
1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 26, 28, 35, 40, 52, 56, 65, 70, 80, 91, 104, 112, 130, 140, 182, 208, 260, 280, 364, 455, 520, 560, 728, 910, 1040, 1456, 1820, 3640, 7280
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7272 and 7280, than apply into the LCM equation.
GCF(7272,7280) = 8
LCM(7272,7280) = ( 7272 × 7280) / 8
LCM(7272,7280) = 52940160 / 8
LCM(7272,7280) = 6617520
(i) The LCM of 7280 and 7272 is associative
LCM of 7272 and 7280 = LCM of 7280 and 7272
1. What is the LCM of 7272 and 7280?
Answer: LCM of 7272 and 7280 is 6617520.
2. What are the Factors of 7272?
Answer: Factors of 7272 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 101, 202, 303, 404, 606, 808, 909, 1212, 1818, 2424, 3636, 7272. There are 24 integers that are factors of 7272. The greatest factor of 7272 is 7272.
3. What are the Factors of 7280?
Answer: Factors of 7280 are 1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 26, 28, 35, 40, 52, 56, 65, 70, 80, 91, 104, 112, 130, 140, 182, 208, 260, 280, 364, 455, 520, 560, 728, 910, 1040, 1456, 1820, 3640, 7280. There are 40 integers that are factors of 7280. The greatest factor of 7280 is 7280.
4. How to Find the LCM of 7272 and 7280?
Answer:
Least Common Multiple of 7272 and 7280 = 6617520
Step 1: Find the prime factorization of 7272
7272 = 2 x 2 x 2 x 3 x 3 x 101
Step 2: Find the prime factorization of 7280
7280 = 2 x 2 x 2 x 2 x 5 x 7 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 = 6617520 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 13 x 101
Step 4: Therefore, the least common multiple of 7272 and 7280 is 6617520.