Least Common Multiple (LCM) of 90 and 167
The least common multiple (LCM) of 90 and 167 is 15030.
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 90 and 167?
First, calculate the GCD of 90 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 167 = 0 remainder 90 |
| 2 | 167 ÷ 90 = 1 remainder 77 |
| 3 | 90 ÷ 77 = 1 remainder 13 |
| 4 | 77 ÷ 13 = 5 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 135 | 2565 |
| 64 and 133 | 8512 |
| 77 and 197 | 15169 |
| 29 and 162 | 4698 |
| 58 and 49 | 2842 |