Least Common Multiple (LCM) of 72 and 53
The least common multiple (LCM) of 72 and 53 is 3816.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 72 and 53?
First, calculate the GCD of 72 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 53 = 1 remainder 19 |
| 2 | 53 ÷ 19 = 2 remainder 15 |
| 3 | 19 ÷ 15 = 1 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 173 | 33216 |
| 144 and 166 | 11952 |
| 144 and 110 | 7920 |
| 106 and 22 | 1166 |
| 110 and 76 | 4180 |