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 |
|---|---|
| 152 and 66 | 5016 |
| 145 and 55 | 1595 |
| 184 and 168 | 3864 |
| 174 and 72 | 2088 |
| 163 and 78 | 12714 |