*You all have studied how to find LCM and HCF in your LP-UP classes. But how many of you can still solve these kind of problems?*There will be problems based on these in various competetive exams. (both direct and indirect). So do your best in this portion.
FACTORS AND MULTIPLES
If a number 'x' divides another number 'y' exactly, then we say that 'x is a factor of 'y' and that 'y is a multiple of x'. For example, 5 is a factor of 10 and therefore 10 is a multiple of 5.
LCM : LEAST COMMON MULTIPLE
LCM is the least non-zero number in common multiples of two or more numbers. Multiple of 4- 4, 8, 12, 16, 20, etc Multiple of 5- 5, 10, 15, 20, 25, etc Multiple of 6- 6, 12, 18, 24, 30, etc *Common multiples of 4 and 5 = 20, 40, etc Least Common Multiple (LCM) = 20 *Common multiples of 5 and 6 = 30, 60, etc Least Common Multiple (LCM) = 30
What is the LCM of 3,5,11 1 3,5,11 3,5,11 .'. LCM = 3 x 5 x 11 = 165
3.
The least square number which is divisible by 3, 5 and 6 is___ The least number divisible by 3,5 and 6 is their LCM, which is 30. Now 30 = 2 x 3 x 5 3 3,5,6 1,5,2 To make it a perfect square, it must be multiplied by 2 x 3 x 5 .'.Required number = 30x2 x3x5 = 900
HCF; HIGHEST COMMON FACTOR
The Highest Common Factor of two or more numbers is the greatest number which divides each of them exactly. For example, find the HCF of 21 and 27. 3 21,27 7,9 .'.HCF = 3
EXAMPLES
1.
Find the HCF of 32, 48, 96 2 32,48,96 2 16,24,48 2 8,12,24 2 4,6,12 2,3,6 .'.HCF = 16
2.
Find the HCF of 3, 5, 11 1 3,5,11 3,5,11 .'.HCF = 1
3.
Find the HCF of 14, 24, 36 2 14,24,36 7,12,18 .'. HCF = 2
TYPE-I
LCM of fractions = LCM of numerators/HCF of denominators HCF of fractions = HCF of numerators/LCM of denominators
EXAMPLES
1.
Find the LCM of 1/3,2/5,3/7 LCM of numerators = LCM of 1, 2, 3 = 1x2x3 = 6 HCF of denominators = HCF of 3, 5, 7 = 1 .'.LCM of the fraction =6/1=6
2.
Find the HCF of 3/4,2/7,1/5 HCF of numerators = HCF of 3, 2,1 = 1 LCM of denominators = LCM of 4, 7, 5 = 140 .'.HCF of the fraction = 1/140
3.
Find the HCF of 12/44,24/20,32/10 HCF of numerators = HCF of 12, 24, 32 2 12,24,32 2 6,12,16 3,6,8 .'.HCF of numerators = 2x2 = 4 LCM of denominators = LCM of 44, 20 and 10 2 44,20,10 2 22,10, 5 5 11,5,5 11, 1,1 LCM of denominators = 2x2x5x11 = 220 HCF of the fraction=4/220=1/55
TYPE - II
Product of two numbers = HCF x LCM of those numbers
EXAMPLES
1.The LCM of two numbers 24 and 36 is 12 Find the HCF HCF =Product of numbers/LCM =24x36 =72 .'.Required HCF = 72 2.The HCF and LCM of two numbers are 120 and 360 respectively. If one number is 120, find the other number. HCF x LCM = Product of numbers 120 x 360 = 120 x second number .'.The other number is 360 3.The HCF and LCM of two numbers are 5 and 100 respectively. The first number when divided by 5 gives the quotient 4. What is the second number? First number = 4 x 5 = 20 Second number =5x100/20=25 4.If the HCF and LCM of two fractions are 1/10 and 3 respectively and one of the fraction is 1/2, find the other one. LCFx HCF =Product of numbers 1/10*3 =1/2 x other number The other fraction=3/10/1/2=3/5
POINTS TO REMEMBER
*LCM of given numbers would be either the of the highest or highest of the number *HCF of given numbers would be either lowest or lower
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