3つの与えられた数の最小公倍数を求める問題です。問題(1)から(10)まであります。

1. 問題の内容

3つの与えられた数の最小公倍数を求める問題です。問題(1)から(10)まであります。

2. 解き方の手順

最小公倍数（LCM）を求めるには、それぞれの数を素因数分解し、各素因数の最大の指数を取って掛け合わせます。

(1) 4, 12, 18

$4 = 2^2$

$12 = 2^2 \times 3$

$18 = 2 \times 3^2$

LCM = $2^2 \times 3^2 = 4 \times 9 = 36$

(2) 12, 18, 20

$12 = 2^2 \times 3$

$18 = 2 \times 3^2$

$20 = 2^2 \times 5$

LCM = $2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180$

(3) 16, 18, 24

$16 = 2^4$

$18 = 2 \times 3^2$

$24 = 2^3 \times 3$

LCM = $2^4 \times 3^2 = 16 \times 9 = 144$

(4) 32, 36, 42

$32 = 2^5$

$36 = 2^2 \times 3^2$

$42 = 2 \times 3 \times 7$

LCM = $2^5 \times 3^2 \times 7 = 32 \times 9 \times 7 = 2016$

(5) 48, 60, 96

$48 = 2^4 \times 3$

$60 = 2^2 \times 3 \times 5$

$96 = 2^5 \times 3$

LCM = $2^5 \times 3 \times 5 = 32 \times 3 \times 5 = 480$

(6) 9, 15, 18

$9 = 3^2$

$15 = 3 \times 5$

$18 = 2 \times 3^2$

LCM = $2 \times 3^2 \times 5 = 2 \times 9 \times 5 = 90$

(7) 12, 60, 69

$12 = 2^2 \times 3$

$60 = 2^2 \times 3 \times 5$

$69 = 3 \times 23$

LCM = $2^2 \times 3 \times 5 \times 23 = 4 \times 3 \times 5 \times 23 = 1380$

(8) 72, 108, 360

$72 = 2^3 \times 3^2$

$108 = 2^2 \times 3^3$

$360 = 2^3 \times 3^2 \times 5$

LCM = $2^3 \times 3^3 \times 5 = 8 \times 27 \times 5 = 1080$

(9) $2^2 \times 3 \times 5, 2^3 \times 3^2, 2 \times 3 \times 5^2$

LCM = $2^3 \times 3^2 \times 5^2 = 8 \times 9 \times 25 = 1800$

(10) $a^2 \times b^3 \times c, a^3 \times c^2, a^4 \times b \times c^2$

LCM = $a^4 \times b^3 \times c^2$

3. 最終的な答え

(1) 36

(2) 180

(3) 144

(4) 2016

(5) 480

(6) 90

(7) 1380

(8) 1080

(9) 1800

(10) $a^4b^3c^2$