Question

Find the LCM of each numbers 3,8,12,15

Answer 1

120

Explanation:

Method 1 ; Using prime factors ;

`3,\:8,\:12,\:15\\\\\mathrm{Prime\:factorization\:of\:}3:\quad 3\\\mathrm{Prime\:factorization\:of\:}8:\quad 2*\:2*\:2\\\mathrm{Prime\:factorization\:of\:}12:\quad 2*\:2*\:3\\\mathrm{Prime\:factorization\:of\:}15:\quad 3*\:5\\\\=3* \:2* \:2* \:2* \:5\\=120`

Method 2 ; Using Multipliers

`\mathrm{The\:multipliers\:of\:}3\\3,\:6,\:9,\:12,\:15,\:18,\:21,\:24,\:27,\:\\30,\:33,\:36,\:39,\:42,\:45,\:48,\:51,\:\\54,\:57,\:60,\:63,\:66,\:69,\:72,\:75,\:\\78,\:81,\:84,\:87,\:90,\:93,\:96,\:99,\:102,\:105,\:108,\:111\\114,\:117,\:120,\:123,\:126,\:129\\`

`\mathrm{The\:multipliers\:of\:}8\\\\=8,\:16,\:24,\:32,\:40,\:48,\:56,\:64,\:72,\\\:80,\:88,\:96,\:104,\:112,\:120,\:128,\:136,\:\\144,\:152,\:160,\:168,\:176,\:184`

`\mathrm{The\:multipliers\:of\:}12\\\\=12,\:24,\:36,\:48,\:60,\:72,\:84,\:96,\:108,\\\:120,\:132,\:144,\:156,\:168,\:180,\:192,\:204,\\\:216,\:228,\:240,\:252,\:264,\:276,\:288,\:\\\\\\\mathrm{The\:multipliers\:of\:}15\\=15,\:30,\:45,\:60,\:75,\:90,\:105,\:120,\\\:135,\:150,\:165,\:180,\:195,\:210,\:225,\\\:240,\:255,\:270,\:285,\:300,\:315,\:330,\:`

`\mathrm{The\:smallest\:common\:number\:is}\\=120`