Least Common Multiple (LCM) of 32 and 72
The least common multiple (LCM) of 32 and 72 is 288.
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 32 and 72?
First, calculate the GCD of 32 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 72 = 0 remainder 32 |
| 2 | 72 ÷ 32 = 2 remainder 8 |
| 3 | 32 ÷ 8 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 164 | 23452 |
| 62 and 40 | 1240 |
| 108 and 59 | 6372 |
| 188 and 117 | 21996 |
| 192 and 180 | 2880 |