Least Common Multiple (LCM) of 161 and 100
The least common multiple (LCM) of 161 and 100 is 16100.
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 161 and 100?
First, calculate the GCD of 161 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 161 ÷ 100 = 1 remainder 61 |
| 2 | 100 ÷ 61 = 1 remainder 39 |
| 3 | 61 ÷ 39 = 1 remainder 22 |
| 4 | 39 ÷ 22 = 1 remainder 17 |
| 5 | 22 ÷ 17 = 1 remainder 5 |
| 6 | 17 ÷ 5 = 3 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 173 | 20760 |
| 143 and 154 | 2002 |
| 174 and 95 | 16530 |
| 128 and 167 | 21376 |
| 139 and 64 | 8896 |