Least Common Multiple (LCM) of 72 and 46
The least common multiple (LCM) of 72 and 46 is 1656.
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 46?
First, calculate the GCD of 72 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 46 = 1 remainder 26 |
| 2 | 46 ÷ 26 = 1 remainder 20 |
| 3 | 26 ÷ 20 = 1 remainder 6 |
| 4 | 20 ÷ 6 = 3 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 113 | 1130 |
| 80 and 54 | 2160 |
| 191 and 193 | 36863 |
| 144 and 170 | 12240 |
| 100 and 75 | 300 |