Least Common Multiple (LCM) of 167 and 106
The least common multiple (LCM) of 167 and 106 is 17702.
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 106?
First, calculate the GCD of 167 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 106 = 1 remainder 61 |
| 2 | 106 ÷ 61 = 1 remainder 45 |
| 3 | 61 ÷ 45 = 1 remainder 16 |
| 4 | 45 ÷ 16 = 2 remainder 13 |
| 5 | 16 ÷ 13 = 1 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 130 | 2080 |
| 168 and 162 | 4536 |
| 32 and 88 | 352 |
| 21 and 170 | 3570 |
| 69 and 15 | 345 |