Misalkan m bilangan asli terkecil sehingga hasil dari M1/6 x 2 1/2 x 3 1/3 x 4 1/4 merupakan

Pertanyaan:

Misalkan m bilangan asli terkecil sehingga hasil dari M1/6 x 2 1/2 x 3 1/3 x 4 1/4 merupakan bilangan asli. Banyak faktor dari m adalah

Untuk mencari m m m terkecil agar m ⋅ 1 6 ⋅ 2 1 2 ⋅ 3 1 3 ⋅ 4 1 4 m center dot one-sixth center dot 2 and one-half center dot 3 and one-third center dot 4 and one-fourth m ⋅ 1 6 ⋅ 2 1 2 ⋅ 3 1 3 ⋅ 4 1 4 menjadi bilangan asli, kita ubah bentuknya menjadi pecahan biasa: m ⋅ 1 6 ⋅ 5 2 ⋅ 10 3 ⋅ 17 4 = m ⋅ 1 ⋅ 5 ⋅ 10 ⋅ 17 6 ⋅ 2 ⋅ 3 ⋅ 4 = m ⋅ 850 144 = m ⋅ 425 72 m center dot one-sixth center dot five-halves center dot ten-thirds center dot seventeen-fourths equals m center dot the fraction with numerator 1 center dot 5 center dot 10 center dot 17 and denominator 6 center dot 2 center dot 3 center dot 4 end-fraction equals m center dot 850 over 144 end-fraction equals m center dot 425 over 72 end-fraction m ⋅ 1 6 ⋅ 5 2 ⋅ 1 0 3 ⋅ 1 7 4 = m ⋅ 1 ⋅ 5 ⋅ 1 0 ⋅ 1 7 6 ⋅ 2 ⋅ 3 ⋅ 4 = m ⋅ 8 5 0 1 4 4 = m ⋅ 4 2 5 7 2 . Agar hasilnya bilangan asli, m m m harus bisa membagi penyebut 72 , jadi m m m adalah 72, dan banyak faktor dari m = 72 m equals 72 m = 7 2 adalah 12, yaitu 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Jadi, banyak faktor dari m m m adalah 12.