Least Common Multiple (LCM) of 100 and 157
The least common multiple (LCM) of 100 and 157 is 15700.
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 100 and 157?
First, calculate the GCD of 100 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 157 = 0 remainder 100 |
| 2 | 157 ÷ 100 = 1 remainder 57 |
| 3 | 100 ÷ 57 = 1 remainder 43 |
| 4 | 57 ÷ 43 = 1 remainder 14 |
| 5 | 43 ÷ 14 = 3 remainder 1 |
| 6 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 114 | 5586 |
| 110 and 196 | 10780 |
| 75 and 186 | 4650 |
| 123 and 46 | 5658 |
| 69 and 160 | 11040 |