Question

甲數(shù)是乙數(shù)的3倍，甲、乙兩數(shù)的和是32，求甲、乙兩數(shù)的最大公因數(shù)和最小公倍數(shù)．

Answer 1

考點：求幾個數(shù)的最大公因數(shù)的方法,求幾個數(shù)的最小公倍數(shù)的方法

專題：數(shù)的整除

分析：根據(jù)甲數(shù)是乙數(shù)的3倍，甲、乙兩數(shù)的和是32，設乙數(shù)是x，則甲數(shù)是3x，3x+x=32，解答x=8，即甲乙兩個數(shù)是24和8，甲數(shù)是乙數(shù)的3倍，說明甲數(shù)是乙數(shù)的整數(shù)倍，求兩個數(shù)為倍數(shù)關系時的最大公約數(shù)：兩個數(shù)為倍數(shù)關系，最大公約數(shù)為較小的數(shù)；最小公倍數(shù)是為較大的數(shù)由此解答問題即可．

解答： 解：設乙數(shù)是x，則甲數(shù)是3x，
3x+x=32
  4x=32
   x=8
3×8=24
24和8是倍數(shù)關系，所以它們的最大公因數(shù)是8，最小公倍數(shù)是24．
答：甲、乙兩數(shù)的最大公因數(shù)是8，最小公倍數(shù)是24．

點評：此題主要考查求兩個數(shù)為倍數(shù)關系時的最大公約數(shù)：兩個數(shù)為倍數(shù)關系，最大公約數(shù)為較小的數(shù)．