Least Common Multiple (LCM) of 68 and 110
The least common multiple (LCM) of 68 and 110 is 3740.
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 68 and 110?
First, calculate the GCD of 68 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 110 = 0 remainder 68 |
| 2 | 110 ÷ 68 = 1 remainder 42 |
| 3 | 68 ÷ 42 = 1 remainder 26 |
| 4 | 42 ÷ 26 = 1 remainder 16 |
| 5 | 26 ÷ 16 = 1 remainder 10 |
| 6 | 16 ÷ 10 = 1 remainder 6 |
| 7 | 10 ÷ 6 = 1 remainder 4 |
| 8 | 6 ÷ 4 = 1 remainder 2 |
| 9 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 68 | 2992 |
| 151 and 98 | 14798 |
| 154 and 88 | 616 |
| 145 and 61 | 8845 |
| 42 and 36 | 252 |