PEA 202 A Lecture 2 HCF AND LCM

PEA 202 A – Lecture #2 HCF AND LCM PEA 202 Analytical Skills- . .

Factors and Multiples: If number a divided another number b exactly, we say that a is a factor of b. In this case, b is called a multiple of a. PEA 202 Analytical Skills- . .

Highest Common Factor (H. C. F. ) or Greatest Common Measure(G. C. M. ) or Greatest Common Divisor (G. C. D. ) The H. C. F. of two or more than two numbers is the greatest number that divided each of them exactly. o. Now, Suppose we have to find the H. C. F. of three numbers, then, H. C. F. of three numbers = H. C. F. of [(H. C. F. of any two) and (the third number)] Similarly, the H. C. F. of more than three numbers may be obtained. PEA 202 Analytical Skills- . .

Least Common Multiple (L. C. M. ) The least number which is exactly divisible by each one of the given numbers is called their L. C. M. PEA 202 Analytical Skills- . .

PEA 202 Analytical Skills- . .

HCF and LCM Problem Solving How can you tell if a word problem requires you to use Highest Common Factor or Least Common Multiple to solve? PEA 202 Analytical Skills- . .

Q 2. 1 : Application of HCF Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips? How wide should she cut the strips so that they are the largest possible equal lengths. PEA 202 Analytical Skills- . .

HCF Word Problem Solution 2 l 72 2 l 90 2 l 36 3 l 45 2 l 18 3 l 15 3 l 9 5 l 5 3 l 3 1 1 72 = 2 x 2 x 3 90 = 2 x 3 x 5 HCF = 2 x 3 = 18 Samantha should cut each piece to be 18 inches wide PEA 202 Analytical Skills- . .

Q 2. 2 : Application of HCF In a school Boys are 289 and Girls are 340. Divide in different sections such that each section has equal no. of students and each section has either boys or girls. What are the minimum no. of sections that are required? PEA 202 Analytical Skills- No of students in a section have to be maximum . .

HCF(289, 340)=17 To get sections of boys and sections of girls : We will have to divide: Boys=289/17=17 Girls=340/17=20 Total no of sections required: 20+17=37 PEA 202 Analytical Skills- . .

Practice Example Rosa is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the largest size tile she can use? PEA 202 Analytical Skills- Quick yak: Question of HCF. . .

Practice P 2. 1 PEA 202 Analytical Skills- 2 l 16 2 l 24 2 l 8 2 l 4 2 l 2 2 l 12 2 l 6 3 l 3 1 1 16 = 2 x 2 x 2 24 = 2 x 2 x 3 HCF = 2 x 2 = 8 The largest size tile that Rosa can use is tile of 8 inches. . .

If it is an LCM Problem What is the question asking us? ü Do we have an event that is or will be repeating over and over? ü Will we have to purchase or get multiple items in order to have enough? ü Are we trying to figure out when something will happen again at the same time? PEA 202 Analytical Skills- . .

Q 2. 2 : Application of LCM Ben exercises every 12 days and Isabel every 8 days. Ben and Isabel both exercised today. How many days will it be until they exercise together again? This problem can be solved using Least Common Multiple. We are trying to figure out when will be the next time they are exercising together. Find the LCM of 12 and 8. PEA 202 Analytical Skills- . .

LCM Word Problem Solution PEA 202 Analytical Skills- 2 l 12 2 l 8 2 l 6 3 l 3 2 l 4 2 l 2 1 1 12 = 2 x 3 8 = 2 x 2 LCM = 2 x 2 x 3 = 24 Ben and Isabel would exercise on the same day every 24 days. . .

A, B, C start at the same time in the same direction to run around a circular stadium. A complete a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point? LCM of 252, 308 and 198=2772 So A, B, C will meet again at the starting point in 2772 sec i. e. 46 min 12 sec. PEA 202 Analytical Skills- . .

Four bells toll after interval of 8, 9, 12 & 15 min. If they toll together at 3 pm when will they toll together next? LCM(8, 9, 12, 15)=360 minutes or 6 hour After every 6 hours, So After 3 pm they will rang at 9 pm PEA 202 Analytical Skills- . .

Practice Example Two bikers are riding a circular path. The first rider completes a round in 12 minutes. The second rider completes a round in 18 minutes. If they both started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point? PEA 202 Analytical Skills- . .

2 l 12 2 l 18 2 l 6 3 l 3 3 l 9 3 l 3 1 1 12 = 2 x 3 18 = 2 x 3 LCM = 2 x 3 x 2 x 3 = 36 Both bikers will meet after 36 minutes. Points To Remember: LCM: Minimum No , Least No , Smaller No HCF: Maximum No , Greatest possible , Longest PEA 202 Analytical Skills- . .

PEA 202 Analytical Skills- Next Class: AVERAGE . .