Least Common Multiple (LCM) of 63 and 167
The least common multiple (LCM) of 63 and 167 is 10521.
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 63 and 167?
First, calculate the GCD of 63 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 167 = 0 remainder 63 |
| 2 | 167 ÷ 63 = 2 remainder 41 |
| 3 | 63 ÷ 41 = 1 remainder 22 |
| 4 | 41 ÷ 22 = 1 remainder 19 |
| 5 | 22 ÷ 19 = 1 remainder 3 |
| 6 | 19 ÷ 3 = 6 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 178 | 15130 |
| 101 and 168 | 16968 |
| 192 and 137 | 26304 |
| 140 and 84 | 420 |
| 70 and 200 | 1400 |