Least Common Multiple (LCM) of 10 and 67
The least common multiple (LCM) of 10 and 67 is 670.
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 10 and 67?
First, calculate the GCD of 10 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 67 = 0 remainder 10 |
| 2 | 67 ÷ 10 = 6 remainder 7 |
| 3 | 10 ÷ 7 = 1 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 101 | 13938 |
| 107 and 185 | 19795 |
| 30 and 32 | 480 |
| 117 and 100 | 11700 |
| 148 and 196 | 7252 |