LCM and HCF
LCM and HCF is a Aptitude concept from the MPSC syllabus, tested in 4 past MPSC questions across 4 exam years between 2015 and 2025. Below are those real questions with their correct answers and explanations, plus the concepts worth being comfortable with first.
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मेजवानीसाठी जमलेल्या कुटुंबियांनी दोघात मिळून एक भाताचे भांडे, तिघात मिळून एक डाळीचे भांडे, पाचात मिळून एक भाजीचे भांडे आणि सहा जणांन मिळून एक श्रीखंडाचे भांडे, याप्रमाणे एकूण 108 भांडी पदार्थ मागवले. यामुळे कोणताही पदार्थ जास्त झाला वा कमी पडला नाही तर एकूण किती कुटुंबिय मेजवानीला उपस्थित होते ? Relatives who had gathered for a party had one bowl of rice between two, one bowl of dal among three, one bowl of vegetable among five and one bowl of shreekhand among six. In all they ordered 108 bowls of eatables; and no food was wasted or was it short. How many relatives were present for the party ?
Let total relatives be x. Bowls equation: x/2 + x/3 + x/5 + x/6 = 108. Taking LCM (30), (15x + 10x + 6x + 5x)/30 = 108 => 36x/30 = 108 => x = 90.
जर 357*25* या संखेेला 3 आणि 5 ने भाग जातो, तर अनुक्रमे एकक व हजार स्थानासाठी, उचित अंकजोडी निवडा. (1) 0, 4 (2) 5, 4 (3) 5, 6 (4) 0, 6 If the number 357*25* is divisible by both 3 and 5, then select the appropriate pair of digits in units and thousandth place respectively. (1) 0, 4 (2) 5, 4 (3) 5, 6 (4) 0, 6
For divisibility by 5, the units place must be 0 or 5. For divisibility by 3, the sum of all digits must be divisible by 3. Testing option (3) with units=5 and thousandth=6 satisfies both rules.
खालील संख्येपैकी किती संख्यांना 273 ने भाग जात नाही ? 546, 1156, 3003, 3564, 5733, 3822, 9605, 8736 How many of the following numbers are not divisible by 273 ? 546, 1156, 3003, 3564, 5733, 3822, 9605, 8736
To check divisibility by 273, we can check divisibility by its coprime factors 3 and 91 (or 3, 7, and 13). Testing each number helps identify how many are not divisible, resulting in the correct count of 2 numbers.
दोन संख्यांचा लसावि हा त्यांच्या मसाविच्या 45 पट आहे. जर एक संख्या 125 असून त्यांच्या मसावि आणि लसाविची बेरीज 1150 आहे, तर दुसरी संख्या _______ . The LCM of two numbers is 45 times their HCF. If one of the number is 125 and sum of their HCF and LCM is 1150, then the other number is _______ .
Given LCM = 45 * HCF and LCM + HCF = 1150, we get 46 * HCF = 1150, so HCF = 25 and LCM = 1125. Using Product = LCM * HCF, second number = (25 * 1125) / 125 = 225.