HCF AND LCM.pptx related to maths with examples

maths

1. HCF AND LCM

2. PRIME FACTORIZATION It is the expression of a given number as theproduct of prime numbers. It can be done using factor tree method ordivision method. Fundamental Theorem of Arithmetic states that every composite number has only one factorization .

3. FACTOR TREE METHOD Draw the factor tree and write down the prime factorisation of the followingnumbers

4. PRIME FACTORIZATION THROUGH DIVISION METHOD STEPS Divide the number with a prime numberwhich will divide it exactly. Continue dividing the quotient until you get aquotient which is a prime number

5. HCF (HIGHEST COMMON FACTOR) Highest common factor (H.C.F) of two or more numbers is the greatest number which divides each of them exactly. Thereare many methods to find them. 1 .listing the factors 2 .HCF by Prime Factorization 3 .HCF by Common division method 4 . HCF by long division method.

6. FIND THE HCF OF FOLLOWING NUMBERS USINGTHE METHOD OF LISTING FACTORS . 24,30 24- 1,2,3,4,6,8,12,24 30- 1,2,3,5,6,10,15,30 COMMON FACTORS OF 24 AND 30- 1,2,3,6 HIGHEST COMMON FACTOR- 6 24,72 24-1,2,3,4,6,8,12,24 72-1,2,3,4,8,9,18,24,36,72 COMMON FACTORS of 24and 72 are 1,2,3,4,8,24 Highest common factor- 24

7. Find the HCF of following numbers using themethod of Prime factorization . Step 1: find the prime factors of givennumbers . Step 2:find the common factors and circlethem . Step 3 multiply the common factors.

8. 30,96 Prime factorization of 30- 2x3x5 Prime factorization of 96- 2x2x2x2x3x2 Hcf -2x3= 6

9. LCM(LOWEST COMMON MULTIPLE) The lowest common multiple of two or more numbers is the lowest of theircommon multiples. It is either equal to or greater than the numbers. The two methods to find LCM are 1. Prime Factorization 2. Common division

10. LCM THROUGH PRIME FACTORIZATION Step 1- Do the prime factorization of all the numbers. Step 2- Express it in terms of powers. Step 3- Multiply the highest powers of each number.

11. FIND THE LCM USING PRIME FACTORIZATION. 72,90 Prime Factorization of 72-2x2x2x3x3 = 2 ³ x 3² Prime Factorization of 90 - 2x5x3x3 = 2 ¹ x 5 ¹ x 3 ² LCM of 72 and 90 = 2 ³ x 3²x5 ¹ =2x2x2x3x3x5=360

12. b) 16,30,42 Prime factorization of 16= 2x2x2x2=2 ⁴ Prime factorization of 30=2x3x5=2 ¹ x3 ¹ x5 ¹ prime factorization of 42= 2x3x7=2 ¹ x3 ¹ x7 ¹ l cm of 16,30 and 42 =2 ⁴ x3 ¹ x5 ¹ x7 ¹ 2x2x2x2x3x5x7 =4x4x15x7=16x105= 1680

13. RELATIONSHIP BETWEEN HCF AND LCM The product of two numbers is the product of their HCFand LCM. a x b= HCF x LCM a = HCF x LCM/b b = HCF x LCM/a HCF= a xb /LCM LCM= a xb /HCF

14. The HCF of two numbers is 12 and their product is 4320. What is their LCM? If one of thenumbers is 60, what is the other number? HCF = 12 Ax B=4320 LCM= AXB/HCF = 4320/12 = 360 ONE NUMBER=60 THE OTHER NUMBER= 4320/60 =72 OR B= HCF X LCM/A = 12X 360/60 = 4320/60 =72

15. The HCF and LCM of two numbers is 15 and 450 respectively. If one number is 75, whatis the other number? HCF= 15 LCM= 450 A= 75 B= HCFX LCM/A =15X450/75 = 90

16. THANK YOU