Least Common Multiple (LCM) of 101 and 168
The least common multiple (LCM) of 101 and 168 is 16968.
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 101 and 168?
First, calculate the GCD of 101 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 168 = 0 remainder 101 |
| 2 | 168 ÷ 101 = 1 remainder 67 |
| 3 | 101 ÷ 67 = 1 remainder 34 |
| 4 | 67 ÷ 34 = 1 remainder 33 |
| 5 | 34 ÷ 33 = 1 remainder 1 |
| 6 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 99 | 13563 |
| 63 and 26 | 1638 |
| 105 and 74 | 7770 |
| 197 and 96 | 18912 |
| 117 and 157 | 18369 |