The lcm is the “lowest common denominator” (lcd) that can be used before fractions can be added, subtracted or compared. The lcm of more than two integers is also well-defined: it is the smallest positive integer that is divisible by each of them.

Real life example : Ram exercises every 12 days and Deepika every 8 days. This problem can be solved using Least Common Multiple because we are trying to figure out when the soonest (Least) time will be that as the event of exercising continues (Multiple), it will occur at the same time (Common).

The smallest positive number that is a multiple of two or more numbers. Example: the Least Common Multiple of 3 and 5 is 15. Because 15 is a multiple of 3 and also a multiple of 5 and it is the smallest number like that. 3 and 5 have other common multiples such as 30, 45, etc, but they are all larger than 15.

Let us consider some of the word problems on l.c.m. (least common multiple).

1. Find the lowest number which is exactly divisible by 18 and 24.
2. Find the lowest number which is less by 5 to be divided by 16, 24 and 36 exactly.
3. Find the lowest number which is more by 6 to be divided by 25, 40 and 60 exactly.

LCM is the product of maximum occurrences of each prime factor in the given numbers. Step 3: So L C M 12,18 = 2 × 2 × 3 × 3 × 5 = 180 seconds = 180/60 = 3 minutes.

Sometimes in such questions, the common remainder can also be asked. You can divide any of the numbers given by HCF (41 ¸ 10) and find the remainder to be equal to 1. L.C.M. of 2, 3 and 6 = 6 ; H.C.F. of 5, 10 and 25 = 5. Thus, the LCM of these three fractions will be 6/5.

What are Applications of LCM and HCF. To split things into smaller sections. To equally distribute any number of sets of items into their largest grouping. To figure out how many people we can invite.

4) H.C.F/G.C.F: (Highest Common Factor / Greatest Common Factor). H.C.F of two or more numbers is the greatest number which divides each number exactly. 5) L.C.M.: (Lowest common multiple). The least number exactly divisible by each one of the given numbers is called least common multiple….Hint:

When we have to find a number larger than given numbers, then we find LCM. If we have to find smaller number, then we find HCF .

HCF-HIGHEST COMMON FACTOR and LCM-LEAST COMMON MULTIPLE.

One way to find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

The concept of L.C.M. is important to solve problems related to racetracks, traffic lights, etc. The applications of H.C.F. are calculating the largest size of tile, the largest tape to measure the land, the maximum scale to measure length etc.

The H.C.F. defines the greatest factor present in between given two or more numbers, whereas L.C.M. defines the least number which is exactly divisible by two or more numbers. H.C.F. is also called the greatest common factor (GCF) and LCM is also called the Least Common Divisor.

The Greatest Common Factor (also known as GCF) is the largest number that divides evenly into each number in a given set of numbers. The Least Common Multiple (also known as LCM) is the smallest positive multiple that is common to two or more numbers.

Answer: LCM of 15 and 20 is 60.

The greatest common divisor of two integers, also known as GCD, is the greatest positive integer that divides the two integers. The least common multiple , also known as the LCM, is the smallest number that is divisible by both integer a and b.

What is the LCM of 25 and 25? The LCM of 25 and 25 is 25.

The LCM of 20 and 20 is 20.

Therefore, the LCM of 3 and 30 is 30.