Least Common Multiple (LCM) of 101 and 158
The least common multiple (LCM) of 101 and 158 is 15958.
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 158?
First, calculate the GCD of 101 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 158 = 0 remainder 101 |
| 2 | 158 ÷ 101 = 1 remainder 57 |
| 3 | 101 ÷ 57 = 1 remainder 44 |
| 4 | 57 ÷ 44 = 1 remainder 13 |
| 5 | 44 ÷ 13 = 3 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 133 | 14630 |
| 141 and 142 | 20022 |
| 17 and 53 | 901 |
| 161 and 28 | 644 |
| 10 and 114 | 570 |