
Least Common Multiple (LCM) of 67 and 40
The least common multiple (LCM) of 67 and 40 is 2680.
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 40?
First, calculate the GCD of 67 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 67 ÷ 40 = 1 remainder 27 |
2 | 40 ÷ 27 = 1 remainder 13 |
3 | 27 ÷ 13 = 2 remainder 1 |
4 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
130 and 19 | 2470 |
62 and 101 | 6262 |
169 and 163 | 27547 |
106 and 130 | 6890 |
45 and 125 | 1125 |