Least Common Multiple (LCM) of 36 and 72
The least common multiple (LCM) of 36 and 72 is 72.
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 36 and 72?
First, calculate the GCD of 36 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 72 = 0 remainder 36 |
| 2 | 72 ÷ 36 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 76 | 4788 |
| 175 and 32 | 5600 |
| 99 and 20 | 1980 |
| 123 and 135 | 5535 |
| 138 and 108 | 2484 |