Least Common Multiple (LCM) of 137 and 166
The least common multiple (LCM) of 137 and 166 is 22742.
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 137 and 166?
First, calculate the GCD of 137 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 166 = 0 remainder 137 |
| 2 | 166 ÷ 137 = 1 remainder 29 |
| 3 | 137 ÷ 29 = 4 remainder 21 |
| 4 | 29 ÷ 21 = 1 remainder 8 |
| 5 | 21 ÷ 8 = 2 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 167 | 10521 |
| 127 and 116 | 14732 |
| 180 and 182 | 16380 |
| 22 and 105 | 2310 |
| 179 and 132 | 23628 |