Question

19．已知甲數(shù)=2×3×3×5×7，乙數(shù)=2×2×5×5×7，甲數(shù)和乙數(shù)的最小公倍數(shù)是6300；最大公因數(shù)是70．

Answer 1

分析 求最大公因數(shù)也就是這幾個數(shù)的公有質(zhì)因數(shù)的連乘積，最小公倍數(shù)是公有質(zhì)因數(shù)與獨有質(zhì)因數(shù)的連乘積．

解答 解：已知甲數(shù)=2×3×3×5×7，乙數(shù)=2×2×5×5×7，
甲數(shù)和乙數(shù)的最小公倍數(shù)是2×2×3×3×5×5×7=6300；最大公因數(shù)是2×5×7=70．
故答案為：6300，70．

點評 此題主要考查求兩個數(shù)的最大公因數(shù)與最小公倍數(shù)的方法：最大公因數(shù)是兩個數(shù)的公有質(zhì)因數(shù)的連乘積，最小公倍數(shù)是公有質(zhì)因數(shù)與獨有質(zhì)因數(shù)的連乘積．