Least Common Multiple (LCM) of 72 and 111
The least common multiple (LCM) of 72 and 111 is 2664.
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 111?
First, calculate the GCD of 72 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 111 = 0 remainder 72 |
| 2 | 111 ÷ 72 = 1 remainder 39 |
| 3 | 72 ÷ 39 = 1 remainder 33 |
| 4 | 39 ÷ 33 = 1 remainder 6 |
| 5 | 33 ÷ 6 = 5 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 115 | 22080 |
| 81 and 67 | 5427 |
| 116 and 43 | 4988 |
| 123 and 25 | 3075 |
| 187 and 81 | 15147 |