Least Common Multiple (LCM) of 110 and 72
The least common multiple (LCM) of 110 and 72 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 110 and 72?
First, calculate the GCD of 110 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 72 = 1 remainder 38 |
| 2 | 72 ÷ 38 = 1 remainder 34 |
| 3 | 38 ÷ 34 = 1 remainder 4 |
| 4 | 34 ÷ 4 = 8 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 28 | 2604 |
| 53 and 62 | 3286 |
| 29 and 146 | 4234 |
| 161 and 184 | 1288 |
| 188 and 174 | 16356 |