Least Common Multiple (LCM) of 158 and 67
The least common multiple (LCM) of 158 and 67 is 10586.
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 158 and 67?
First, calculate the GCD of 158 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 158 ÷ 67 = 2 remainder 24 |
| 2 | 67 ÷ 24 = 2 remainder 19 |
| 3 | 24 ÷ 19 = 1 remainder 5 |
| 4 | 19 ÷ 5 = 3 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 35 | 5985 |
| 48 and 151 | 7248 |
| 27 and 21 | 189 |
| 147 and 114 | 5586 |
| 54 and 57 | 1026 |