Least Common Multiple (LCM) of 67 and 119
The least common multiple (LCM) of 67 and 119 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 67 and 119?
First, calculate the GCD of 67 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 119 = 0 remainder 67 |
| 2 | 119 ÷ 67 = 1 remainder 52 |
| 3 | 67 ÷ 52 = 1 remainder 15 |
| 4 | 52 ÷ 15 = 3 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 31 | 2077 |
| 172 and 94 | 8084 |
| 190 and 105 | 3990 |
| 103 and 138 | 14214 |
| 136 and 27 | 3672 |