Students of a middle school section in a school are divided into groups of 9,
12, and 15 for three different projects. In case 2 students were left after
grouping. Find the exact number of students in the middle school section if
the number lies between 300 to 400.
Answers
Answer:
Answer is 360. See the image for explained solution.
Concept:
In mathematics, Least Common Multiple is referred to by its entire name, whereas Highest Common Factor is its complete name. The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the H.C.F. describes the biggest factor existing between any given pair of two or more numbers. LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).
We have two key techniques—the division method and the prime factorization approach—for determining H.C.F. and L.C.M. In our earlier classes, we learnt about both approaches. The quickest way to determine H.C.F. and L.C.M. is by using a division approach.
HCF xLCM = multiplication of the no.s
Given:
Students of a middle school section in a school are divided into groups of 9,12, and 15 for three different projects. In case 2 students were left after
grouping.
Find:
Find the exact number of students in the middle school section if
the number lies between 300 to 400.
Solution:
Case 1 : group of 9 each
Let no. of groups be x
Total no. of studenst =9x+2------------i
Case 2: group of 12 each
Let no. of groups be y
Total no. of studenst be= 12x+2-------------ii
Case 3: Group of 15 each
Let no. of groups be z
Total no. of studnets =15x+2---------------iii
Since eq i, ii and iii are equal
We can write
px+2=12y+2=15z+2
9x=12y=15z
LCM of 9,12, 15=180
Hence, no. of students be multiple of 180
since no. of student s lies between 300 and 400
Therefore, no. of students =180 x 2 =360
Therefore, the no. of students =360
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