Least Common Multiple (LCM) of 163 and 101
The least common multiple (LCM) of 163 and 101 is 16463.
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 163 and 101?
First, calculate the GCD of 163 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 101 = 1 remainder 62 |
| 2 | 101 ÷ 62 = 1 remainder 39 |
| 3 | 62 ÷ 39 = 1 remainder 23 |
| 4 | 39 ÷ 23 = 1 remainder 16 |
| 5 | 23 ÷ 16 = 1 remainder 7 |
| 6 | 16 ÷ 7 = 2 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 23 | 2461 |
| 22 and 51 | 1122 |
| 148 and 86 | 6364 |
| 178 and 10 | 890 |
| 54 and 103 | 5562 |