Question

Find the L.C.M of the numbers 15, 25, 35?

Answer 1

Hint: We start solving the problem by recalling the definition of L.C.M (Least Common Multiple) of two or more numbers as the smallest number that is exactly divisible by all of those two or more numbers. We then make use of the ladder method to find the L.C.M of the given numbers by dividing the terms with the number that is at least factor of two of the given numbers. We then multiply the numbers that cannot be further divisible by any prime factors to get the required value of L.C.M.

Complete step by step answer:
According to the problem, we are asked to find the L.C.M (Least Common Multiple) of the numbers 15, 25, 35.
Let us recall the definition of L.C.M (Least Common Multiple) of two or more of the given numbers.
We know that L.C.M (Least Common Multiple) of two or more numbers is defined as the smallest number that is exactly divisible by all of those two or more numbers.
Let us find the L.C.M of the given numbers 15, 25, 35 using the ladder method which is as shown below:
 $ \begin{align}
  & 5\left| \!{\underline {\,
  15,25,35 \,}} \right. \\
 & \left| \!{\underline {\,
  3,5,7 \,}} \right. \\
\end{align} $ .
Let us find the L.C.M by multiplying the remaining numbers.
So, the L.C.M (Least Common Multiple) of the numbers 15, 25, 35 is $ 5\times 3\times 5\times 7=525 $ .
∴ The L.C.M (Least Common Multiple) of the numbers 15, 25, 35 is 525.

Note:
We should divide the given terms with the prime numbers in the ladder method if and only if at least two of the given numbers are divisible by it. We can also find the L.C.M by writing the multiples of all the given numbers first and then finding the least numbers that is common in all of those multiples. Similarly, we can expect problems to find the G.C.F (Greatest Common Factor) for the given numbers.