Least Common Multiple (LCM) of 67 and 145
The least common multiple (LCM) of 67 and 145 is 9715.
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 145?
First, calculate the GCD of 67 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 145 = 0 remainder 67 |
| 2 | 145 ÷ 67 = 2 remainder 11 |
| 3 | 67 ÷ 11 = 6 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 160 | 3360 |
| 126 and 11 | 1386 |
| 93 and 55 | 5115 |
| 38 and 179 | 6802 |
| 105 and 51 | 1785 |