Lagnever AI English

LCM kaise nikalein?

Short mein jawab

Do ya zyaada numbers ka LCM (lowest common multiple) wo sabse chhota number hai jo har number ka multiple ho. Multiples ki list banao jab tak koi common na mile, ya prime factorisation lagao: har prime ko guna karo, har ek ko utni baar jitni sabse zyaada baar wo aata hai. 72 aur 120 ka LCM 360 hai.

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Common multiples

Kisi number ka multiple wo number guna 1, 2, 3 aur aage hai. Do ya zyaada numbers ka common multiple un sabka multiple hota hai. Common multiples un sawaalon ka jawab dete hain jahan cheezon ko milna ho ya saath hona ho. Anshu 6 cm ki pattiyan jodkar toran banaata hai aur Guna 8 cm ki pattiyan jodkar. Agar dono ke toran barabar lambe hon, to lambai 6 ka bhi multiple honi chahiye aur 8 ka bhi.

Anshu ki 6 cm aur Guna ki 8 cm ki pattiyan 24 cm aur 48 cm pe saath khatm hoti hain
6 aur 8 ke common multiples

6 ke multiples: 6, 12, 18, 24, 30, 36, 42, 48 … 8 ke multiples: 8, 16, 24, 32, 40, 48 … Common waale 24, 48, 72 aur aage hain, isliye dono jo sabse chhota toran bana sakte hain wo 24 cm ka hai.

Lowest common multiple

LCM, yaani lowest (ya least) common multiple, common multiples mein sabse chhota hai. Sabse bada common multiple nahi hota: agar 24 common hai, to 48, 72, 96 aur 24 ka har aage ka multiple bhi common hai.

Dohraane waali ghatnaon ke sawaal LCM se hal hote hain. Ek mithai ki dukaan har Monday, yaani har 7 din, school ke bachchon ko gajak baantti hai, aur Kabamai, jise aaj gajak mili, har 10 din mein aati hai. Use dobara gajak sirf us din milegi jo 7 aur 10 dono ka multiple ho, aur aisa pehla din 70 din baad hai. Idli-Vada game mein pehla number jis pe “idli-vada” bola jaata hai, chune gaye do numbers ka LCM hai: 4 aur 6 ke liye 12, aur 7 aur 11 ke liye 77.

Prime factorisation se

14 aur 30 jaise numbers ke multiples ki list lambi ho jaati hai. Prime factorisation jaldi hai. Kisi number ke multiple mein us number ke saare primes hote hain, aur shaayad kuch aur bhi. Isliye common multiple mein har number ka poora factorisation hona chahiye, aur sabse chhote mein kuch extra nahi hota:

  • har wo prime lo jo kisi bhi number mein aata hai;
  • har ek ko utni baar lo jitni sabse zyaada baar wo kisi ek number mein aata hai.
72 aur 120 ko 2s, 3s aur 5s mein toda gaya: LCM teen 2, do 3 aur ek 5 leta hai
72 aur 120 ka LCM = 360

14 = 2 × 7 aur 35 = 5 × 7 ka LCM 2 × 5 × 7 = 70 hai: isme 2 × 7 bhi hai aur 5 × 7 bhi, aur koi prime hataane se inme se ek kho jaayega. 72 = 2 × 2 × 2 × 3 × 3 aur 120 = 2 × 2 × 2 × 3 × 5 ke liye teen 2, do 3 aur ek 5 lo: LCM = 360. 96 = 2 × 2 × 2 × 2 × 2 × 3 aur 360 = 2 × 2 × 2 × 3 × 3 × 5 ke liye paanch 2, do 3 aur ek 5 lo: LCM = 1440. Chhe 2 lene se bhi common multiple milega, par zaroorat se dugna bada.

Dohraane waale patterns

Rangeen sitaaron ki do kataarein: upar har 6 sitaaron pe neela, neeche har 4 pe, jo sitaara 4 aur 16 pe milte hain
Dohraane waale patterns LCM pe milte hain

Jab do patterns har 6 aur har 4 jagah pe dohraate hain, to milti hui jagahein har 12 jagah pe dobara aati hain, jo 6 aur 4 ka LCM hai. Isi soch se pata chalta hai ki har 20 aur 30 minute pe chalne waali do buses agli baar saath kab chalengi (60 minute baad), ya har 8 aur 12 second pe jalne waali do lights agli baar saath kab jalengi (24 second baad).

Kaam ke shortcuts

Agar ek number doosre ka multiple ho, to LCM bada number hai: 3 aur 24 ka LCM 24 hai. Agar do numbers mein koi prime saajha na ho, jaise 8 aur 9, to LCM unka guna, 72, hai. Har haal mein do numbers ka LCM unke guna se zyaada nahi hota, kyunki guna khud ek common multiple hai.

Ye kyun zaroori hai

LCM batata hai ki dohraane waali cheezein dobara kab milengi: ghantiyan, buses, tyohaar, gears aur patterns. Fractions jodne ke liye sabse chhota common denominator bhi yahi deta hai. Ise HCF kaise nikalein? se milaao, aur dono ka rishta HCF aur LCM ka sambandh mein dekho. Textbook ke sawaalon ke jawab Part 2 Chapter 3 ke NCERT solutions mein hain; poore Part 2 Chapter 3 ke notes dekho.

Practice karo

  1. 4 aur 6 ke pehle teen common multiples hain:

    1. (a) 12, 24, 36
    2. (b) 10, 20, 30
    3. (c) 24, 48, 72
    4. (d) 2, 12, 24
    Jawab dekho

    Jawab: (a) 12, 24, 36

  2. 2 × 2 × 3 aur 2 × 3 × 3 ka LCM hai:

    1. (a) 6
    2. (b) 18
    3. (c) 36
    4. (d) 72
    Jawab dekho

    Jawab: (c) 36

  3. Do lights ek saath jalti hain, phir ek har 8 s aur doosri har 12 s pe jalti hai. Agli baar saath jalengi:

    1. (a) 20 s baad
    2. (b) 24 s baad
    3. (c) 48 s baad
    4. (d) 96 s baad
    Jawab dekho

    Jawab: (b) 24 s baad

  4. Prime factorisation se 18 aur 30 ka LCM nikaalo.

    Jawab dekho

    Jawab: 18 = 2 × 3 × 3 aur 30 = 2 × 3 × 5. Har prime, har ek sabse zyaada baar: 2 × 3 × 3 × 5 = 90.

  5. Kya 6 aur 8 ka koi sabse bada common multiple hai? Kyun?

    Jawab dekho

    Jawab: Nahi. Agar koi number common multiple hai, to uska 2 guna, 3 guna aur aage bhi common multiples hain, isliye list kabhi khatm nahi hoti.

Students ke sawal

LCM kya hai?

Do ya zyaada numbers ka LCM wo sabse chhota number hai jo un sabka multiple ho. 6 ke multiples 6, 12, 18, 24 aur aage hain, aur 8 ke 8, 16, 24 aur aage, isliye 6 aur 8 ka LCM 24 hai.

Lowest common multiple ya least common multiple?

Dono ka matlab ek hi number hai. NCERT book lowest common multiple kehti hai, aur kai books least common multiple: wo sabse chhota number jo diye gaye sabhi numbers ka multiple ho.

Teen numbers ka LCM kaise nikaalein?

Har number ko primes mein todo, har aane waala prime lo, har ek ko utni baar jitni sabse zyaada baar wo kisi ek number mein aata hai, aur guna karo. 4 = 2 × 2, 6 = 2 × 3 aur 10 = 2 × 5 ka LCM 2 × 2 × 3 × 5 = 60 hai.

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