LCM and HCF

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.

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.