Least Common Multiple (LCM) of 67 and 105
The least common multiple (LCM) of 67 and 105 is 7035.
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 105?
First, calculate the GCD of 67 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 105 = 0 remainder 67 |
| 2 | 105 ÷ 67 = 1 remainder 38 |
| 3 | 67 ÷ 38 = 1 remainder 29 |
| 4 | 38 ÷ 29 = 1 remainder 9 |
| 5 | 29 ÷ 9 = 3 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 143 | 17017 |
| 85 and 73 | 6205 |
| 127 and 122 | 15494 |
| 105 and 176 | 18480 |
| 88 and 137 | 12056 |