Least Common Multiple (LCM) of 100 and 168
The least common multiple (LCM) of 100 and 168 is 4200.
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 168?
First, calculate the GCD of 100 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 168 = 0 remainder 100 |
| 2 | 168 ÷ 100 = 1 remainder 68 |
| 3 | 100 ÷ 68 = 1 remainder 32 |
| 4 | 68 ÷ 32 = 2 remainder 4 |
| 5 | 32 ÷ 4 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 184 | 552 |
| 135 and 69 | 3105 |
| 113 and 13 | 1469 |
| 61 and 149 | 9089 |
| 28 and 23 | 644 |