Least Common Multiple (LCM) of 67 and 146
The least common multiple (LCM) of 67 and 146 is 9782.
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 146?
First, calculate the GCD of 67 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 146 = 0 remainder 67 |
| 2 | 146 ÷ 67 = 2 remainder 12 |
| 3 | 67 ÷ 12 = 5 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 145 | 15080 |
| 159 and 154 | 24486 |
| 32 and 195 | 6240 |
| 61 and 184 | 11224 |
| 160 and 167 | 26720 |