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Sabse Chhota, Par Aakhri Nahi!

Class 7 Maths · Chapter 11: Saajha Aadhaar Dhoondhna · NCERT Ganita Prakash section P2 3.2

Seekho

Kabir 6 cm ki pattiyon se aur Zoya 8 cm ki pattiyon se toran banaate hain. Ek jitni lambaai ke liye lambaai 6 ka multiple (6, 12, 18, 24 …) aur 8 ka (8, 16, 24 …) ho. Sabse chhoti 24 cm. Common multiples kabhi khatam nahi (24, 48, 72 …), to sabse bada koi nahi.

LCM(6, 8) = 24

Ye Lowest Common Multiple (LCM) hai. Mithaai ki dukaan har Somvaar (har 7 din) muft gajak deti hai, aur Ishaan har 10 din aata hai. Somvaar se shuru karke ve agli baar LCM(7, 10) = 70 din baad milte hain. 4 aur 6 ke idli–vada khel mein pehla "idli-vada" 12.

LCM(7, 10) = 70

Primes se LCM: multiple mein number ke saare primes hote hain. To common multiple mein dono factorisation hone chahiye. 14 = 2 × 7 aur 35 = 5 × 7: dono ko rakhne wala sabse chhota 2 × 5 × 7 = 70. Har aane wala prime lo, har ek kisi bhi number mein zyaada se zyaada jitni baar.

LCM(14, 35) = 2 × 5 × 7 = 70

96 = 2 × 2 × 2 × 2 × 2 × 3 aur 360 = 2 × 2 × 2 × 3 × 3 × 5. LCM ko paanch 2, do 3 aur ek 5 chahiye: 2⁵ × 3² × 5 = 1440. Milaao: HCF common primes ke kam se kam, LCM saare primes ke zyaada se zyaada leta hai.

LCM(96, 360) = 1440

Explore: common multiples.

  1. Wo numbers tap karo jo 6 aur 8 dono ke multiples hain.

Yaad rakho

  • LCM = sabse chhota common multiple; "phir kab milenge" sawaalon ka jawaab.
  • Prime factorisation se: har prime, har ek zyaada se zyaada baar.

Quick check

36 aur 54 ka LCM?

  1. 108
  2. 18
  3. 1944
  4. 216
Answer

108. 36 = 2² × 3², 54 = 2 × 3³: LCM = 2² × 3³ = 108.

Socho

200 se kam gaayon ka jhund 3, phir 5, phir 7 darwaazon se barabar guzarta hai. Kitni gaayein?

Ek answer

Number 3, 5 aur 7 ka common multiple hai. LCM 105, aur agla 210 bahut zyaada. To 105 gaayein.

Practice

Teen levels (easy, medium, hard) ke naye sawaalon se practice karo, kuch hands-on, hints aur hal ke saath. Topic poora karne ke liye pichhle 5 mein se 4 sahi karo.