LCM (Least Common Multiple) Coding Practice Problems

The (Least Common Multiple) of two numbers is the smallest positive integer that can be divided by both of the numbers.

Computing the LCM

Computing the Least Common Multiple (LCM) of two numbers involves finding the smallest number that is a multiple of both.
The most efficient way to compute the LCM is by using the relationship between LCM and the Greatest Common Divisor (GCD). The formula for LCM is given by:

LCM(a,b) = \frac{( a \times b )} {GCD(a,b)}

By utilizing the GCD, we can compute the LCM efficiently in O(log⁡(min⁡(a,b))) time. This approach is efficient and reduces the problem of finding the LCM by simply computing the GCD and performing multiplication and division. This approach avoids the need for checking each multiple of the numbers individually and provides a direct, optimized way to calculate the least common multiple.

Here is a list of the Top LCM Problems for practice. Problems in this Article are divided into three Levels to practice according to the difficulty level step by step.

Coding Problems Based on LCM

• Maximum sum of distinct numbers such that LCM of these numbers is N
• Find the least common multiple (LCM) of given Strings
• LCM of given array elements
• Count common elements in two arrays containing multiples of N and M
• Count of common multiples of two numbers in a range
• Sum of LCM(1, n), LCM(2, n), LCM(3, n), … , LCM(n, n)
• Minimum number of Cuboids required to form a Cube
• Count ordered pairs of numbers with a given LCM
• Find two numbers with given sum and maximum possible LCM
• Minimum possible value of max(A, B) such that LCM(A, B) = C
• Find two numbers with the given LCM and minimum possible difference
• Maximum LCM among all pairs (i, j) of first N natural numbers
• Minimum and Maximum LCM among all pairs (i, j) in range [L, R]
• Minimum length of a rod that can be split into N equal parts that can further be split into given number of equal parts
• Minimum number to be added to minimize LCM of two given numbers
• Generate a pair of integers from a range [L, R] whose LCM also lies within the range
• Find two distinct numbers such that their LCM lies in given range
• Maximize the sum of modulus with every Array element
• Minimum integer such that it leaves a remainder 1 on dividing with any element from the range [2, N]
• Smallest prime giving remainder K when divided by any Array element
• Count of pairs having even and odd LCM from an array
• Smallest number not less than N which is divisible by all digits of N
• Minimum replacement of pairs by their LCM required to reduce given array to its LCM
• Minimum LCM of all pairs in a given array
• Minimum number to be added to minimize LCM of two given numbers
• Find triplet (A, B, C) such that LCM(A, B) + LCM(A, C) + LCM(B, C) equals N
• Range LCM Queries
• Find maximum LCM that can be obtained from four numbers less than or equal to N