Least Common Multiple (LCM) of 30 and 167
The least common multiple (LCM) of 30 and 167 is 5010.
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 30 and 167?
First, calculate the GCD of 30 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 167 = 0 remainder 30 |
| 2 | 167 ÷ 30 = 5 remainder 17 |
| 3 | 30 ÷ 17 = 1 remainder 13 |
| 4 | 17 ÷ 13 = 1 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 143 | 16159 |
| 21 and 20 | 420 |
| 60 and 100 | 300 |
| 125 and 96 | 12000 |
| 95 and 53 | 5035 |