Least Common Multiple (LCM) of 100 and 136
The least common multiple (LCM) of 100 and 136 is 3400.
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 136?
First, calculate the GCD of 100 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 136 = 0 remainder 100 |
| 2 | 136 ÷ 100 = 1 remainder 36 |
| 3 | 100 ÷ 36 = 2 remainder 28 |
| 4 | 36 ÷ 28 = 1 remainder 8 |
| 5 | 28 ÷ 8 = 3 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 35 | 1120 |
| 200 and 15 | 600 |
| 14 and 163 | 2282 |
| 185 and 60 | 2220 |
| 158 and 104 | 8216 |