Least Common Multiple (LCM) of 168 and 67
The least common multiple (LCM) of 168 and 67 is 11256.
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 168 and 67?
First, calculate the GCD of 168 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 67 = 2 remainder 34 |
| 2 | 67 ÷ 34 = 1 remainder 33 |
| 3 | 34 ÷ 33 = 1 remainder 1 |
| 4 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 39 | 546 |
| 149 and 22 | 3278 |
| 50 and 34 | 850 |
| 170 and 104 | 8840 |
| 21 and 103 | 2163 |