Least Common Multiple (LCM) of 67 and 110
The least common multiple (LCM) of 67 and 110 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 67 and 110?
First, calculate the GCD of 67 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 110 = 0 remainder 67 |
| 2 | 110 ÷ 67 = 1 remainder 43 |
| 3 | 67 ÷ 43 = 1 remainder 24 |
| 4 | 43 ÷ 24 = 1 remainder 19 |
| 5 | 24 ÷ 19 = 1 remainder 5 |
| 6 | 19 ÷ 5 = 3 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 11 | 99 |
| 98 and 157 | 15386 |
| 191 and 122 | 23302 |
| 138 and 117 | 5382 |
| 130 and 64 | 4160 |