Least Common Multiple (LCM) of 167 and 101
The least common multiple (LCM) of 167 and 101 is 16867.
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 167 and 101?
First, calculate the GCD of 167 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 101 = 1 remainder 66 |
| 2 | 101 ÷ 66 = 1 remainder 35 |
| 3 | 66 ÷ 35 = 1 remainder 31 |
| 4 | 35 ÷ 31 = 1 remainder 4 |
| 5 | 31 ÷ 4 = 7 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 17 | 2686 |
| 103 and 142 | 14626 |
| 36 and 98 | 1764 |
| 53 and 190 | 10070 |
| 105 and 171 | 5985 |