Least Common Multiple (LCM) of 100 and 167
The least common multiple (LCM) of 100 and 167 is 16700.
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 167?
First, calculate the GCD of 100 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 167 = 0 remainder 100 |
| 2 | 167 ÷ 100 = 1 remainder 67 |
| 3 | 100 ÷ 67 = 1 remainder 33 |
| 4 | 67 ÷ 33 = 2 remainder 1 |
| 5 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 193 | 38407 |
| 145 and 46 | 6670 |
| 34 and 112 | 1904 |
| 74 and 171 | 12654 |
| 78 and 56 | 2184 |