Least Common Multiple (LCM) of 59 and 167
The least common multiple (LCM) of 59 and 167 is 9853.
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 59 and 167?
First, calculate the GCD of 59 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 167 = 0 remainder 59 |
| 2 | 167 ÷ 59 = 2 remainder 49 |
| 3 | 59 ÷ 49 = 1 remainder 10 |
| 4 | 49 ÷ 10 = 4 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 40 | 7560 |
| 56 and 137 | 7672 |
| 23 and 163 | 3749 |
| 75 and 53 | 3975 |
| 50 and 96 | 2400 |