Least Common Multiple (LCM) of 41 and 72
The least common multiple (LCM) of 41 and 72 is 2952.
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 41 and 72?
First, calculate the GCD of 41 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 72 = 0 remainder 41 |
| 2 | 72 ÷ 41 = 1 remainder 31 |
| 3 | 41 ÷ 31 = 1 remainder 10 |
| 4 | 31 ÷ 10 = 3 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 23 | 2047 |
| 171 and 24 | 1368 |
| 74 and 104 | 3848 |
| 163 and 192 | 31296 |
| 107 and 63 | 6741 |