Least Common Multiple (LCM) of 72 and 110
The least common multiple (LCM) of 72 and 110 is 3960.
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 110?
First, calculate the GCD of 72 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 110 = 0 remainder 72 |
| 2 | 110 ÷ 72 = 1 remainder 38 |
| 3 | 72 ÷ 38 = 1 remainder 34 |
| 4 | 38 ÷ 34 = 1 remainder 4 |
| 5 | 34 ÷ 4 = 8 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 142 | 27406 |
| 101 and 154 | 15554 |
| 75 and 93 | 2325 |
| 57 and 84 | 1596 |
| 132 and 44 | 132 |