Least Common Multiple (LCM) of 67 and 120
The least common multiple (LCM) of 67 and 120 is 8040.
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 120?
First, calculate the GCD of 67 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 120 = 0 remainder 67 |
| 2 | 120 ÷ 67 = 1 remainder 53 |
| 3 | 67 ÷ 53 = 1 remainder 14 |
| 4 | 53 ÷ 14 = 3 remainder 11 |
| 5 | 14 ÷ 11 = 1 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 83 | 12201 |
| 105 and 144 | 5040 |
| 168 and 199 | 33432 |
| 50 and 93 | 4650 |
| 126 and 107 | 13482 |