Least Common Multiple (LCM) of 110 and 67
The least common multiple (LCM) of 110 and 67 is 7370.
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 67?
First, calculate the GCD of 110 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 67 = 1 remainder 43 |
| 2 | 67 ÷ 43 = 1 remainder 24 |
| 3 | 43 ÷ 24 = 1 remainder 19 |
| 4 | 24 ÷ 19 = 1 remainder 5 |
| 5 | 19 ÷ 5 = 3 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 90 | 360 |
| 17 and 121 | 2057 |
| 119 and 173 | 20587 |
| 65 and 53 | 3445 |
| 10 and 19 | 190 |