Least Common Multiple (LCM) of 162 and 100
The least common multiple (LCM) of 162 and 100 is 8100.
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 162 and 100?
First, calculate the GCD of 162 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 100 = 1 remainder 62 |
| 2 | 100 ÷ 62 = 1 remainder 38 |
| 3 | 62 ÷ 38 = 1 remainder 24 |
| 4 | 38 ÷ 24 = 1 remainder 14 |
| 5 | 24 ÷ 14 = 1 remainder 10 |
| 6 | 14 ÷ 10 = 1 remainder 4 |
| 7 | 10 ÷ 4 = 2 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 103 | 12051 |
| 150 and 52 | 3900 |
| 31 and 19 | 589 |
| 175 and 58 | 10150 |
| 113 and 58 | 6554 |