Least Common Multiple (LCM) of 119 and 67
The least common multiple (LCM) of 119 and 67 is 7973.
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 119 and 67?
First, calculate the GCD of 119 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 67 = 1 remainder 52 |
| 2 | 67 ÷ 52 = 1 remainder 15 |
| 3 | 52 ÷ 15 = 3 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 101 | 19493 |
| 105 and 26 | 2730 |
| 200 and 182 | 18200 |
| 188 and 38 | 3572 |
| 157 and 174 | 27318 |