#1**+1 **

Let m and n be positive integers such that m = 24n + 51. What is the largest possible value of the greatest common divisor of 2m and 3n?

m=3(8n+17)

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

m | 3*25 | 3*33 | 3*41 | 3*49 | 3*57 | 3*65 | 3*73 | 3*81 | 3*89 |

3n | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 |

2m | 2*3*25 | 2*3*33 | 2*3*41 | 2*3*49 | 2*3*57 | 2*3*65 | 2*3*73 | 2*3*81 | 2*3*89 |

HCF | 3 | 6 | 3 | 6 | 3 | 6 | 3 | 6 | 3 |

Well

if n is odd the HCF is 3

if n is even the HCF is 6

Melody
57 mins ago

Apr 20, 2018