Least Common Multiple (LCM) of 100 and 162
The least common multiple (LCM) of 100 and 162 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 100 and 162?
First, calculate the GCD of 100 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 162 = 0 remainder 100 |
| 2 | 162 ÷ 100 = 1 remainder 62 |
| 3 | 100 ÷ 62 = 1 remainder 38 |
| 4 | 62 ÷ 38 = 1 remainder 24 |
| 5 | 38 ÷ 24 = 1 remainder 14 |
| 6 | 24 ÷ 14 = 1 remainder 10 |
| 7 | 14 ÷ 10 = 1 remainder 4 |
| 8 | 10 ÷ 4 = 2 remainder 2 |
| 9 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 75 | 450 |
| 124 and 138 | 8556 |
| 35 and 178 | 6230 |
| 42 and 94 | 1974 |
| 32 and 22 | 352 |