Least Common Multiple (LCM) of 67 and 100
The least common multiple (LCM) of 67 and 100 is 6700.
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 67 and 100?
First, calculate the GCD of 67 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 100 = 0 remainder 67 |
| 2 | 100 ÷ 67 = 1 remainder 33 |
| 3 | 67 ÷ 33 = 2 remainder 1 |
| 4 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 141 | 3948 |
| 105 and 132 | 4620 |
| 91 and 35 | 455 |
| 144 and 14 | 1008 |
| 189 and 33 | 2079 |