Least Common Multiple (LCM) of 100 and 67
The least common multiple (LCM) of 100 and 67 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 100 and 67?
First, calculate the GCD of 100 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 67 = 1 remainder 33 |
| 2 | 67 ÷ 33 = 2 remainder 1 |
| 3 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 174 | 870 |
| 138 and 194 | 13386 |
| 182 and 22 | 2002 |
| 123 and 16 | 1968 |
| 46 and 10 | 230 |