Note for Problems on H.C.F and L.C.M - H.C.F and L.C.M By Placement Factory
- Problems on H.C.F and L.C.M - H.C.F and L.C.M
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Factor : A number is said to be a factor of another number it divides the other number exactly. E.g. 2 and 3 are factors of 6. Common Factor : A common Factor of two or more numbers is a number that divides each of them exactly. E.g. 3 is a common factor of 9, 15, 21, 36. Highest Common Factor (HCF) : HCF of two or more numbers is the greatest factor which divides each of them exactly. E.g. 12 is the HCF of 24 and 36. Note : Greatest Common Measure is the another name for Highest Common Factor (HCF). Methods of Finding HCF Prime Factorization method : First of all the numbers are broken into prime factors and then all the common factors of all the numbers are multiplied to get the HCF. Q Find the HCF of 42, 70 and 126. Ans Division Method – The greater is divided by the smaller number, then the divisor is divided by the remainder, then the remainder is divided by the next remainder and the process continues until no remainder is left. The last divisor is the required HCF. In case of Calculation of HCF of more than two numbers, first of all HCF of any two numbers is calculated and then we find the HCF of this HCF and the third number and so on. The last HCF will be the required HCF. Q Find the HCF of 42, 70 and 84. HCF & LCM Page 1
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14 is the HCF of 42 and 70 Now, The required HCF=14 HCF of Decimals : Firstly make ( if necessary ) the same number of decimal places in all the given numbers, then their HCF is found as if they were integers and then as many decimal places are marked off as there are in each of the numbers. Q. Find HCF of 17.40, 0.45 and 15. Ans: The given numbers are equivalent to 17.40, 0.45 and 15.00. HCF of 1740, 45 and 1500 is 15. Required HCF =0.15 HCF of Fractions : The HCF of two or more fractions is the highest fraction which is exactly divisible by each of the fraction. First of all the given fraction are expressed in their lowest terms. Then HCF= HCF of numerators / LCM of denominators HCF & LCM Page 2
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Multiple: A multiple of a number is a number which is exactly divisible by the number. E.g. 12 is a multiple of 3. Common Multiple : A common multiple of two or more numbers is a number which is exactly divisible by each of them. e.g.= 12 is a common multiple of 2, 3, 4 and 6. Least Common Multiple (LCM)- The LCM of two or more given numbers is the least number which is exactly divisible by each of them. e.g. 12 is a common multiple of 3 and 4. 24 is a common multiple of 3 and 4 36 is a common multiple of 3 and 4. Hence 12 is the least common multiple (LCM) of 3 and 4. Calculation of LCM 1 Prime Factorization Method – In this method, the given numbers are resolved into their prime factors and then the product of the highest power of all the factors that occur in the given numbers are found. This product is the LCM. Q Find the LCM of 8, 12 and 15. Ans: HCF & LCM Page 3
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2 Division by Prime Factor Method : Numbers are written down in a line and are separated by commas. Then they are divided by any prime numbers which will exactly divide at least two of them. Set down the quotients and the undivided numbers in a line below the first. Repeat the process until we get a line of numbers which are prime to each other. The product of all the divisors and the numbers in the least line is the required LCM. Q Find the LCM of 8 ,12 and 15. LCM of Decimals : First of all make ( if necessary) the same number of decimal places in all the given numbers, then find their LCM as if they were integers, and mark in the result as many decimal places as there in each of the numbers. Q Find the LCM of 0.6, 9.6 and 0.36. Ans : The given numbers are equivalent to 0.60, 9.60 and 0.36 Now, LCM of 60, 960 and 36 is 2880 Required LCM = 28.80 LCM of Fractions : The LCM of two or more fractions is the least fraction or integer which is exactly divisible by each of them. HCF & LCM Page 4
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