Least Common Multiple (LCM) of 67 and 148
The least common multiple (LCM) of 67 and 148 is 9916.
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 148?
First, calculate the GCD of 67 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 148 = 0 remainder 67 |
| 2 | 148 ÷ 67 = 2 remainder 14 |
| 3 | 67 ÷ 14 = 4 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 76 | 1292 |
| 114 and 16 | 912 |
| 115 and 28 | 3220 |
| 38 and 95 | 190 |
| 172 and 144 | 6192 |