Least Common Multiple (LCM) of 167 and 21
The least common multiple (LCM) of 167 and 21 is 3507.
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 167 and 21?
First, calculate the GCD of 167 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 21 = 7 remainder 20 |
| 2 | 21 ÷ 20 = 1 remainder 1 |
| 3 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 62 | 6634 |
| 110 and 16 | 880 |
| 115 and 74 | 8510 |
| 141 and 138 | 6486 |
| 14 and 177 | 2478 |