Least Common Multiple (LCM) of 167 and 104
The least common multiple (LCM) of 167 and 104 is 17368.
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 104?
First, calculate the GCD of 167 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 104 = 1 remainder 63 |
| 2 | 104 ÷ 63 = 1 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 |
|---|---|
| 60 and 116 | 1740 |
| 113 and 138 | 15594 |
| 79 and 116 | 9164 |
| 193 and 97 | 18721 |
| 170 and 70 | 1190 |