Question

Find the least common multiple (LCM) of 7 and 12.

Answer 1

84

Explanation:

Method 1 ; Prime factorization

`7 ,12\\\mathrm{Prime\:factorization\:of\:}7:\quad 7\\\mathrm{Prime\:factorization\:of\:}12:\quad 2\cdot \:2\cdot \:3\\= 847*\:2*\:2*\:3\\= 84`

Method 2 ;Multipliers

`\mathrm{The\:multipliers\:of\:}7\\=7,\:14,\:21,\:28,\:35,\:42,\:49,\:56,\:63,\:70,\:77,\:84,\:91,\:98,\:105...\\\\\mathrm{The\:multipliers\:of\:}12\\=12,\:24,\:36,\:48,\:60,\:72,\:84,\:96,\:108,\:120,\:132,\:144,\:156,\:168,\:180...\\\\\mathrm{The\:smallest\:common\:number\:is} \\=84`

Method 3 ; Using GCD

`lcm\left(a,\:b\right)=(|a\cdot b|)/(gcd\left(a,\:b\right))\\\\\mathrm{Greatest\:Common\:Divisor\:of\:}7,\:12:\quad 1\\=(\left|7*\:12\right|)/(1)\\\\= 84`