Least Common Multiple (LCM) of 35 and 167
The least common multiple (LCM) of 35 and 167 is 5845.
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 35 and 167?
First, calculate the GCD of 35 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 167 = 0 remainder 35 |
| 2 | 167 ÷ 35 = 4 remainder 27 |
| 3 | 35 ÷ 27 = 1 remainder 8 |
| 4 | 27 ÷ 8 = 3 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 57 | 11172 |
| 99 and 96 | 3168 |
| 101 and 142 | 14342 |
| 140 and 178 | 12460 |
| 180 and 137 | 24660 |