Least Common Multiple (LCM) of 67 and 59
The least common multiple (LCM) of 67 and 59 is 3953.
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 59?
First, calculate the GCD of 67 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 59 = 1 remainder 8 |
| 2 | 59 ÷ 8 = 7 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 178 | 28302 |
| 137 and 81 | 11097 |
| 129 and 175 | 22575 |
| 100 and 70 | 700 |
| 147 and 192 | 9408 |