The Units digit??

To find unit digit in product $(3547)^{153}\times(251)^{72}$ we find unit digits of $(3547)^{153} \& (251)^{72}$ respectively.

1] $(3547)^{153}$ cyclicity of 7 is 4 .

Remainder when 153 is divided by 4 is 1 .

Hence , last digit of $(3547)^{153}$ will be $7^1$ = 7

2] $(251)^{72}$ cyclicity of 1 is 1

Hence,unit digit of $(251)^{72}$ is 1

Hence, unit digit of $(3547)^{153}\times(251)^{72}$ is $7\times1=\boxed7$

unit digit of 3547^153=7, and unit digit of 251^72 is 1, hence the unit digit of 3547^153 251^72 is 7 1=7.