Least Common Multiple (LCM) of 68 and 119
The least common multiple (LCM) of 68 and 119 is 476.
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 119?
First, calculate the GCD of 68 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 119 = 0 remainder 68 |
| 2 | 119 ÷ 68 = 1 remainder 51 |
| 3 | 68 ÷ 51 = 1 remainder 17 |
| 4 | 51 ÷ 17 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 169 | 5239 |
| 75 and 50 | 150 |
| 20 and 162 | 1620 |
| 129 and 110 | 14190 |
| 195 and 159 | 10335 |